Charles D. Bailyn
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691148823
- eISBN:
- 9781400850563
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691148823.003.0009
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter looks at the detection of black holes through gravitational waves. While further improvements can be expected in the ability to detect and measure electromagnetic radiation, it is ...
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This chapter looks at the detection of black holes through gravitational waves. While further improvements can be expected in the ability to detect and measure electromagnetic radiation, it is possible that the next great advances in observational astrophysics will come from the detection of other kinds of information altogether. Currently, there is a great excitement about the possibility of directly detecting an entirely new “celestial messenger,” namely, gravitational radiation. The existence of gravitational waves is a prediction of general relativity, and current technology is very close to being able to detect them directly. The strongest sources of gravitational radiation are expected to be merging black holes. Since such mergers are expected to occur, both between stellar-mass and supermassive black holes, the detection of gravitational radiation would provide a new way not only to explore gravitational physics but also to look for and to study celestial black holes.Less
This chapter looks at the detection of black holes through gravitational waves. While further improvements can be expected in the ability to detect and measure electromagnetic radiation, it is possible that the next great advances in observational astrophysics will come from the detection of other kinds of information altogether. Currently, there is a great excitement about the possibility of directly detecting an entirely new “celestial messenger,” namely, gravitational radiation. The existence of gravitational waves is a prediction of general relativity, and current technology is very close to being able to detect them directly. The strongest sources of gravitational radiation are expected to be merging black holes. Since such mergers are expected to occur, both between stellar-mass and supermassive black holes, the detection of gravitational radiation would provide a new way not only to explore gravitational physics but also to look for and to study celestial black holes.
Yvonne Choquet-Bruhat
- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0003
- Subject:
- Mathematics, Applied Mathematics
This chapter begins with a discussion of Newton's gravity law. It then covers general relativity, observations and experiments, Einstein's equations, field sources, Lagrangians, fluid sources, ...
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This chapter begins with a discussion of Newton's gravity law. It then covers general relativity, observations and experiments, Einstein's equations, field sources, Lagrangians, fluid sources, Newtonian approximation, Minkowskian approximation, high-frequency gravitational waves, and coupled electromagnetic and gravitational waves.Less
This chapter begins with a discussion of Newton's gravity law. It then covers general relativity, observations and experiments, Einstein's equations, field sources, Lagrangians, fluid sources, Newtonian approximation, Minkowskian approximation, high-frequency gravitational waves, and coupled electromagnetic and gravitational waves.
Ta-Pei Cheng
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199573639
- eISBN:
- 9780191722448
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573639.003.0015
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
In the weak-field limit Einstein's equation can be linearized and it takes on form of the familiar wave equation. Gravitational waves may be viewed as ripples of curvature propagating in a background ...
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In the weak-field limit Einstein's equation can be linearized and it takes on form of the familiar wave equation. Gravitational waves may be viewed as ripples of curvature propagating in a background of flat spacetime. The strategy of detecting such tidal forces by a gravitational wave interferometer is outlined. The rate of energy loss due to the quadrupole radiation by a circulating binary system is calculated, and found in excellent agreement with the observed orbit decay rate of the Hulse-Taylor binary pulsar.Less
In the weak-field limit Einstein's equation can be linearized and it takes on form of the familiar wave equation. Gravitational waves may be viewed as ripples of curvature propagating in a background of flat spacetime. The strategy of detecting such tidal forces by a gravitational wave interferometer is outlined. The rate of energy loss due to the quadrupole radiation by a circulating binary system is calculated, and found in excellent agreement with the observed orbit decay rate of the Hulse-Taylor binary pulsar.
Michele Maggiore
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198570745
- eISBN:
- 9780191717666
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570745.003.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter discusses how gravitational waves emerge from general relativity, and what their properties are. The most straightforward approach is ‘linearized theory’, where the Einstein equations ...
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This chapter discusses how gravitational waves emerge from general relativity, and what their properties are. The most straightforward approach is ‘linearized theory’, where the Einstein equations are expanded around the flat Minkowski metric. It is shown how a wave equation emerges and how the solutions can be put in an especially simple form by an appropriate gauge choice. Using standard tools of general relativity such as the geodesic equation and the equation of the geodesic deviation, how these waves interact with a set of test masses is detailed. The energy and momentum carried by GWs are then computed and discussed. This chapter approaches the problem from a geometric point of view, identifying the energy-momentum tensor of GWs from their effect on the background curvature. Finally, GW propagation in curved space is discussed.Less
This chapter discusses how gravitational waves emerge from general relativity, and what their properties are. The most straightforward approach is ‘linearized theory’, where the Einstein equations are expanded around the flat Minkowski metric. It is shown how a wave equation emerges and how the solutions can be put in an especially simple form by an appropriate gauge choice. Using standard tools of general relativity such as the geodesic equation and the equation of the geodesic deviation, how these waves interact with a set of test masses is detailed. The energy and momentum carried by GWs are then computed and discussed. This chapter approaches the problem from a geometric point of view, identifying the energy-momentum tensor of GWs from their effect on the background curvature. Finally, GW propagation in curved space is discussed.
Miguel Alcubierre
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199205677
- eISBN:
- 9780191709371
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199205677.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Gravitational waves are one of the most important physical phenomena associated with the presence of strong and dynamic gravitational fields, and as such they are of great interest in numerical ...
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Gravitational waves are one of the most important physical phenomena associated with the presence of strong and dynamic gravitational fields, and as such they are of great interest in numerical relativity. There are two main approaches to the extraction of gravitational wave information from a numerical simulation. Traditional approach has been based on the theory of perturbations of a Schwarzschild spacetime developed originally by Regge and Wheeler, Zerilli, and a number of other authors, and later recast as a gauge invariant framework by Moncrief. In recent years, however, it has become increasingly common in numerical relativity to extract gravitational wave information in terms of the components of the Weyl curvature tensor with respect to a frame of null vectors, using what is known as the Newman-Penrose formalism. This chapter presents a brief introduction to both these approaches, and describes how to calculate the energy and momentum radiated by gravitational waves in each case.Less
Gravitational waves are one of the most important physical phenomena associated with the presence of strong and dynamic gravitational fields, and as such they are of great interest in numerical relativity. There are two main approaches to the extraction of gravitational wave information from a numerical simulation. Traditional approach has been based on the theory of perturbations of a Schwarzschild spacetime developed originally by Regge and Wheeler, Zerilli, and a number of other authors, and later recast as a gauge invariant framework by Moncrief. In recent years, however, it has become increasingly common in numerical relativity to extract gravitational wave information in terms of the components of the Weyl curvature tensor with respect to a frame of null vectors, using what is known as the Newman-Penrose formalism. This chapter presents a brief introduction to both these approaches, and describes how to calculate the energy and momentum radiated by gravitational waves in each case.
Yvonne Choquet-Bruhat
- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0011
- Subject:
- Mathematics, Applied Mathematics
This chapter draws on the treatment of progressive waves for non-linear equations used in Sections III.12 and III.13 to construct weak gravitational and electromagnetic waves on a given electrovac ...
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This chapter draws on the treatment of progressive waves for non-linear equations used in Sections III.12 and III.13 to construct weak gravitational and electromagnetic waves on a given electrovac Einsteinian spacetime. Topics covered include quasilinear systems, quasilinear first-order systems, progressive waves in relativistic fluids, quasilinear quasidiagonal second-order systems, non quasidiagonal second-order systems, fields and equations, and strong gravitational waves.Less
This chapter draws on the treatment of progressive waves for non-linear equations used in Sections III.12 and III.13 to construct weak gravitational and electromagnetic waves on a given electrovac Einsteinian spacetime. Topics covered include quasilinear systems, quasilinear first-order systems, progressive waves in relativistic fluids, quasilinear quasidiagonal second-order systems, non quasidiagonal second-order systems, fields and equations, and strong gravitational waves.
Valeri P. Frolov and Andrei Zelnikov
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199692293
- eISBN:
- 9780191731860
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199692293.003.0010
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This Chapter contains a review of many important aspects of modern black hole theory and its applications. It begins with a general definition of a (not‐necessary stationary) black hole and ...
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This Chapter contains a review of many important aspects of modern black hole theory and its applications. It begins with a general definition of a (not‐necessary stationary) black hole and formulation of the most important results on generic properties of black holes, including the Penrose theorem on the structure of the event horizon, the Hawking theorems on the topology and area of the event horizon and black hole uniqueness theorems. Gravitational radiation from black holes in a binary system and modern status and perspectives of the gravitation waves search from black holes and other compact sources are discussed. We also describe black hole models proposed for the explanation of the gamma‐ray bursts. Modeling of black hole properties, in particular their Hawking radiation, in the laboratory experiments is reviewed. We also discuss recent models with large extra dimensions and possibility of micro black hole creation in the collider experiments. This subject is directly connected with the problem of the higher dimensional black holes. Higher dimensional generalization of the Kerr metric, and a variety of new exact solutions for higher dimensional black objects with the non‐spherical topology of the horizon are discussed. The Chapter ends with remarks on two closely related problems on the wormhole and ‘time machine’ existence. It is shown that in order to create and support macroscopic objects of this type a new exotic form of the matter is requires. It seams that this and possible instabilities make the existence of such objects questionable at least at the present state of our knowledge. These and other fascinating open problems are still wait for their solution.Less
This Chapter contains a review of many important aspects of modern black hole theory and its applications. It begins with a general definition of a (not‐necessary stationary) black hole and formulation of the most important results on generic properties of black holes, including the Penrose theorem on the structure of the event horizon, the Hawking theorems on the topology and area of the event horizon and black hole uniqueness theorems. Gravitational radiation from black holes in a binary system and modern status and perspectives of the gravitation waves search from black holes and other compact sources are discussed. We also describe black hole models proposed for the explanation of the gamma‐ray bursts. Modeling of black hole properties, in particular their Hawking radiation, in the laboratory experiments is reviewed. We also discuss recent models with large extra dimensions and possibility of micro black hole creation in the collider experiments. This subject is directly connected with the problem of the higher dimensional black holes. Higher dimensional generalization of the Kerr metric, and a variety of new exact solutions for higher dimensional black objects with the non‐spherical topology of the horizon are discussed. The Chapter ends with remarks on two closely related problems on the wormhole and ‘time machine’ existence. It is shown that in order to create and support macroscopic objects of this type a new exotic form of the matter is requires. It seams that this and possible instabilities make the existence of such objects questionable at least at the present state of our knowledge. These and other fascinating open problems are still wait for their solution.
Joshua S. Bloom
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691145570
- eISBN:
- 9781400837007
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691145570.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter focuses on how gamma-ray bursts (GRBs) are emerging as unique tools in the study of broad areas of astronomy and physics by virtue of their special properties. The unassailable fact ...
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This chapter focuses on how gamma-ray bursts (GRBs) are emerging as unique tools in the study of broad areas of astronomy and physics by virtue of their special properties. The unassailable fact about GRBs that makes them such great probes is that they are fantastically bright and so can be seen to the farthest reaches of the observable Universe. In parallel with the ongoing study of GRB events and progenitors, new lines of inquiry have burgeoned: using GRBs as unique probes of the Universe in ways that are almost completely divorced from the nature of GRBs themselves. Topics discussed include studies of gas, dust, and galaxies; the history of star formation; measuring reionization and the first objects in the universe; neutrinos, gravitational waves, and cosmic rays; quantum gravity and the expansion of the universe; and the future of GRBs.Less
This chapter focuses on how gamma-ray bursts (GRBs) are emerging as unique tools in the study of broad areas of astronomy and physics by virtue of their special properties. The unassailable fact about GRBs that makes them such great probes is that they are fantastically bright and so can be seen to the farthest reaches of the observable Universe. In parallel with the ongoing study of GRB events and progenitors, new lines of inquiry have burgeoned: using GRBs as unique probes of the Universe in ways that are almost completely divorced from the nature of GRBs themselves. Topics discussed include studies of gas, dust, and galaxies; the history of star formation; measuring reionization and the first objects in the universe; neutrinos, gravitational waves, and cosmic rays; quantum gravity and the expansion of the universe; and the future of GRBs.
Miguel Alcubierre
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199205677
- eISBN:
- 9780191709371
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199205677.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book introduces the modern field of 3+1 numerical relativity. It has been written in a way as to be as self-contained as possible, and assumes a basic knowledge of special relativity. Starting ...
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This book introduces the modern field of 3+1 numerical relativity. It has been written in a way as to be as self-contained as possible, and assumes a basic knowledge of special relativity. Starting from a brief introduction to general relativity, it discusses the different concepts and tools necessary for the fully consistent numerical simulation of relativistic astrophysical systems, with strong and dynamical gravitational fields. Among the topics discussed in detail are the following: the initial data problem, hyperbolic reductions of the field equations, gauge conditions, the evolution of black hole space-times, relativistic hydrodynamics, gravitational wave extraction, and numerical methods. There is also a final chapter with examples of some simple numerical space-times.Less
This book introduces the modern field of 3+1 numerical relativity. It has been written in a way as to be as self-contained as possible, and assumes a basic knowledge of special relativity. Starting from a brief introduction to general relativity, it discusses the different concepts and tools necessary for the fully consistent numerical simulation of relativistic astrophysical systems, with strong and dynamical gravitational fields. Among the topics discussed in detail are the following: the initial data problem, hyperbolic reductions of the field equations, gauge conditions, the evolution of black hole space-times, relativistic hydrodynamics, gravitational wave extraction, and numerical methods. There is also a final chapter with examples of some simple numerical space-times.
Hanoch Gutfreund and Jürgen Renn
- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691174631
- eISBN:
- 9781400888689
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691174631.003.0009
- Subject:
- Physics, History of Physics
This chapter addresses one of the key themes of modern general relativity: gravitational waves. In 1916, Einstein performed the first relevant calculations, including a first derivation of the ...
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This chapter addresses one of the key themes of modern general relativity: gravitational waves. In 1916, Einstein performed the first relevant calculations, including a first derivation of the celebrated quadrupole formula, which contained a mistake that he corrected in 1918. The corrected formula became the basis for the long-term search and the first observational verification of these waves. These calculations provoked a discussion about the reality of these waves, which continued well into the 1950s and beyond. What is worth emphasizing is how Einstein's predominant interest in this phenomenon, which developed immediately after the completion of his general theory, had faded away completely by the time he delivered the Princeton lectures.Less
This chapter addresses one of the key themes of modern general relativity: gravitational waves. In 1916, Einstein performed the first relevant calculations, including a first derivation of the celebrated quadrupole formula, which contained a mistake that he corrected in 1918. The corrected formula became the basis for the long-term search and the first observational verification of these waves. These calculations provoked a discussion about the reality of these waves, which continued well into the 1950s and beyond. What is worth emphasizing is how Einstein's predominant interest in this phenomenon, which developed immediately after the completion of his general theory, had faded away completely by the time he delivered the Princeton lectures.
Valeri P. Frolov and Andrei Zelnikov
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199692293
- eISBN:
- 9780191731860
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199692293.003.0005
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
In this Chapter we ‘derive’ the Einstein equations, study their weak field approximation, and briefly discuss gravitational waves and their generation. We finish the Chapter by remarks on the higher ...
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In this Chapter we ‘derive’ the Einstein equations, study their weak field approximation, and briefly discuss gravitational waves and their generation. We finish the Chapter by remarks on the higher dimensional gravity, spacetimes with large extra dimensions, and their properties.Less
In this Chapter we ‘derive’ the Einstein equations, study their weak field approximation, and briefly discuss gravitational waves and their generation. We finish the Chapter by remarks on the higher dimensional gravity, spacetimes with large extra dimensions, and their properties.
Charles D. Bailyn
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691148823
- eISBN:
- 9781400850563
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691148823.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
Emitting no radiation or any other kind of information, black holes mark the edge of the universe—both physically and in our scientific understanding. Yet astronomers have found clear evidence for ...
More
Emitting no radiation or any other kind of information, black holes mark the edge of the universe—both physically and in our scientific understanding. Yet astronomers have found clear evidence for the existence of black holes, employing the same tools and techniques used to explore other celestial objects. This book goes behind the theory and physics of black holes to describe how astronomers are observing these enigmatic objects and developing a remarkably detailed picture of what they look like and how they interact with their surroundings. Accessible to undergraduates and others with some knowledge of introductory college-level physics, this book presents the techniques used to identify and measure the mass and spin of celestial black holes. These key measurements demonstrate the existence of two kinds of black holes, those with masses a few times that of a typical star, and those with masses comparable to whole galaxies—supermassive black holes. The book provides a detailed account of the nature, formation, and growth of both kinds of black holes. The book also describes the possibility of observing theoretically predicted phenomena such as gravitational waves, wormholes, and Hawking radiation. A cutting-edge introduction to a subject that was once on the border between physics and science fiction, this book shows how black holes are becoming routine objects of empirical scientific study.Less
Emitting no radiation or any other kind of information, black holes mark the edge of the universe—both physically and in our scientific understanding. Yet astronomers have found clear evidence for the existence of black holes, employing the same tools and techniques used to explore other celestial objects. This book goes behind the theory and physics of black holes to describe how astronomers are observing these enigmatic objects and developing a remarkably detailed picture of what they look like and how they interact with their surroundings. Accessible to undergraduates and others with some knowledge of introductory college-level physics, this book presents the techniques used to identify and measure the mass and spin of celestial black holes. These key measurements demonstrate the existence of two kinds of black holes, those with masses a few times that of a typical star, and those with masses comparable to whole galaxies—supermassive black holes. The book provides a detailed account of the nature, formation, and growth of both kinds of black holes. The book also describes the possibility of observing theoretically predicted phenomena such as gravitational waves, wormholes, and Hawking radiation. A cutting-edge introduction to a subject that was once on the border between physics and science fiction, this book shows how black holes are becoming routine objects of empirical scientific study.
H. Asada, T. Futamase, and P. A. Hogan
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199584109
- eISBN:
- 9780191723421
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199584109.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
A subject closely related to equations of motion is the gravitational physics of few body systems. First, the chapter reviews choreographic solutions for the N‐body problem in Newton's theory of ...
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A subject closely related to equations of motion is the gravitational physics of few body systems. First, the chapter reviews choreographic solutions for the N‐body problem in Newton's theory of gravity. A solution is called choreographic if each massive particle moves periodically in a single closed orbit. One such choreographic solution is a stable figure‐eight orbit for a three‐body system. The chapter describes connections between the choreographic solutions and the gravitational waves that are predicted by Einstein's theory of general relativity and thus general relativistic choreography is discussed. General relativistic effects cause, for example to binary orbits, a complicated flower‐like pattern by the periastron advance. It is not trivial whether general relativistic effects admit a choreographic solution such as the figure eight. At least at the first and second post Newtonian orders (neglecting dissipative effects starting at the second and half post Newtonian order) the tricky figure eight remarkably remains true.Less
A subject closely related to equations of motion is the gravitational physics of few body systems. First, the chapter reviews choreographic solutions for the N‐body problem in Newton's theory of gravity. A solution is called choreographic if each massive particle moves periodically in a single closed orbit. One such choreographic solution is a stable figure‐eight orbit for a three‐body system. The chapter describes connections between the choreographic solutions and the gravitational waves that are predicted by Einstein's theory of general relativity and thus general relativistic choreography is discussed. General relativistic effects cause, for example to binary orbits, a complicated flower‐like pattern by the periastron advance. It is not trivial whether general relativistic effects admit a choreographic solution such as the figure eight. At least at the first and second post Newtonian orders (neglecting dissipative effects starting at the second and half post Newtonian order) the tricky figure eight remarkably remains true.
Claude Barrabès and Peter A. Hogan
- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199680696
- eISBN:
- 9780191760662
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199680696.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This book is aimed at students who have completed a final year undergraduate course on general relativity and supplemented it with additional techniques by individual study or in a taught MSc ...
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This book is aimed at students who have completed a final year undergraduate course on general relativity and supplemented it with additional techniques by individual study or in a taught MSc programme. The additional technical knowledge required involves the Cartan calculus, the tetrad formalism including aspects of the Newman–Penrose formalism, the Ehlers–Sachs theory of null geodesic congruences, and the Petrov classification of gravitational fields. Each chapter could be used as a basis for an advanced undergraduate or early postgraduate project. The topics covered fall under three general headings: Gravitational waves in vacuo and in a cosmological setting, equations of motion with particular emphasis on spinning particles, and black holes. These are not individual applications of the techniques mentioned above. The techniques are available for use in whole or in part (mainly in part) as each situation demands.Less
This book is aimed at students who have completed a final year undergraduate course on general relativity and supplemented it with additional techniques by individual study or in a taught MSc programme. The additional technical knowledge required involves the Cartan calculus, the tetrad formalism including aspects of the Newman–Penrose formalism, the Ehlers–Sachs theory of null geodesic congruences, and the Petrov classification of gravitational fields. Each chapter could be used as a basis for an advanced undergraduate or early postgraduate project. The topics covered fall under three general headings: Gravitational waves in vacuo and in a cosmological setting, equations of motion with particular emphasis on spinning particles, and black holes. These are not individual applications of the techniques mentioned above. The techniques are available for use in whole or in part (mainly in part) as each situation demands.
Nicholas Manton and Nicholas Mee
- Published in print:
- 2017
- Published Online:
- July 2017
- ISBN:
- 9780198795933
- eISBN:
- 9780191837111
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198795933.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter presents the physical motivation for general relativity, derives the Einstein field equation and gives concise derivations of the main results of the theory. It begins with the ...
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This chapter presents the physical motivation for general relativity, derives the Einstein field equation and gives concise derivations of the main results of the theory. It begins with the equivalence principle, tidal forces in Newtonian gravity and their connection to curved spacetime geometry. This leads to a derivation of the field equation. Tests of general relativity are considered: Mercury’s perihelion advance, gravitational redshift, the deflection of starlight and gravitational lenses. The exterior and interior Schwarzschild solutions are discussed. Eddington–Finkelstein coordinates are used to describe objects falling into non-rotating black holes. The Kerr metric is used to describe rotating black holes and their astrophysical consequences. Gravitational waves are described and used to explain the orbital decay of binary neutron stars. Their recent detection by LIGO and the beginning of a new era of gravitational wave astronomy is discussed. Finally, the gravitational field equations are derived from the Einstein–Hilbert action.Less
This chapter presents the physical motivation for general relativity, derives the Einstein field equation and gives concise derivations of the main results of the theory. It begins with the equivalence principle, tidal forces in Newtonian gravity and their connection to curved spacetime geometry. This leads to a derivation of the field equation. Tests of general relativity are considered: Mercury’s perihelion advance, gravitational redshift, the deflection of starlight and gravitational lenses. The exterior and interior Schwarzschild solutions are discussed. Eddington–Finkelstein coordinates are used to describe objects falling into non-rotating black holes. The Kerr metric is used to describe rotating black holes and their astrophysical consequences. Gravitational waves are described and used to explain the orbital decay of binary neutron stars. Their recent detection by LIGO and the beginning of a new era of gravitational wave astronomy is discussed. Finally, the gravitational field equations are derived from the Einstein–Hilbert action.
Luciano Rezzolla and Olindo Zanotti
- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780198528906
- eISBN:
- 9780191746505
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528906.003.0012
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
The last chapter of the book deals with physical systems whose conditions require the solution both of the Einstein equations and of the hydrodynamics equations. The first examples considered are ...
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The last chapter of the book deals with physical systems whose conditions require the solution both of the Einstein equations and of the hydrodynamics equations. The first examples considered are those of stationary isolated stars, including gravastars and rotating stars, followed by the analysis of compact stars collapsing to a black hole, which are treated both through the dust solution of Oppenheimer–Snyder and through fluid solutions. Since the nonlinearity and complexity of the equations that need to be solved make it increasingly difficult to obtain analytic solutions, the role of numerical simulations becomes increasingly important. Numerical simulations are indeed crucial for the investigation of complex systems such as neutron-star binaries and black-hole–neutron-star binaries, which are treated with an eye on their possible detection through the emission of gravitational waves.Less
The last chapter of the book deals with physical systems whose conditions require the solution both of the Einstein equations and of the hydrodynamics equations. The first examples considered are those of stationary isolated stars, including gravastars and rotating stars, followed by the analysis of compact stars collapsing to a black hole, which are treated both through the dust solution of Oppenheimer–Snyder and through fluid solutions. Since the nonlinearity and complexity of the equations that need to be solved make it increasingly difficult to obtain analytic solutions, the role of numerical simulations becomes increasingly important. Numerical simulations are indeed crucial for the investigation of complex systems such as neutron-star binaries and black-hole–neutron-star binaries, which are treated with an eye on their possible detection through the emission of gravitational waves.
- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199680696
- eISBN:
- 9780191760662
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199680696.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
Starting with plane gravitational waves of arbitrary profile as solutions of Einstein’s vacuum field equations in the linear approximation a sequence of gauge transformations results in a metric ...
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Starting with plane gravitational waves of arbitrary profile as solutions of Einstein’s vacuum field equations in the linear approximation a sequence of gauge transformations results in a metric tensor which is an exact solution of the vacuum field equations. The Khan–Penrose solution of Einstein’s vacuum field equations describing the gravitational field following the head-on collision of plane gravitational impulsive waves is derived. The head-on collision of electromagnetic and gravitational shock waves is discussed with the latter collision resulting in the appearance of ‘dark energy’ in the gravitational field following the collision. High-frequency plane and spherical fronted gravitational waves are also discussed.Less
Starting with plane gravitational waves of arbitrary profile as solutions of Einstein’s vacuum field equations in the linear approximation a sequence of gauge transformations results in a metric tensor which is an exact solution of the vacuum field equations. The Khan–Penrose solution of Einstein’s vacuum field equations describing the gravitational field following the head-on collision of plane gravitational impulsive waves is derived. The head-on collision of electromagnetic and gravitational shock waves is discussed with the latter collision resulting in the appearance of ‘dark energy’ in the gravitational field following the collision. High-frequency plane and spherical fronted gravitational waves are also discussed.
Bahram Mashhoon
- Published in print:
- 2017
- Published Online:
- July 2017
- ISBN:
- 9780198803805
- eISBN:
- 9780191842313
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198803805.003.0009
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics
Gravitational radiation is investigated within the framework of linearized nonlocal gravity. In this theory, linearized gravitational waves are damped as they travel from the source to the receiver. ...
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Gravitational radiation is investigated within the framework of linearized nonlocal gravity. In this theory, linearized gravitational waves are damped as they travel from the source to the receiver. This gravitational memory drag leads to the exponential decay of the wave amplitude. The damping effect could be significant for waves with very long wavelegths comparable to galactic distances. More generally, for gravitational waves with wavelengths comparable to the basic nonlocality lengthscale of order 1 kpc, the nonlocal deviations from general relativity can be significant. However, gravitational waves of current observational interest have wavelengths that are very small in comparison with 1 kpc; in this case, the nonlocal deviations from general relativity essentially average out and can be safely neglected in practice.Less
Gravitational radiation is investigated within the framework of linearized nonlocal gravity. In this theory, linearized gravitational waves are damped as they travel from the source to the receiver. This gravitational memory drag leads to the exponential decay of the wave amplitude. The damping effect could be significant for waves with very long wavelegths comparable to galactic distances. More generally, for gravitational waves with wavelengths comparable to the basic nonlocality lengthscale of order 1 kpc, the nonlocal deviations from general relativity can be significant. However, gravitational waves of current observational interest have wavelengths that are very small in comparison with 1 kpc; in this case, the nonlocal deviations from general relativity essentially average out and can be safely neglected in practice.
Ta-Pei Cheng
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199573639
- eISBN:
- 9780191722448
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573639.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
Einstein's general theory of relativity is introduced in this advanced undergraduate and beginning graduate level textbook. Topics include special relativity, the principle of equivalence, Riemannian ...
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Einstein's general theory of relativity is introduced in this advanced undergraduate and beginning graduate level textbook. Topics include special relativity, the principle of equivalence, Riemannian geometry and tensor analysis, Einstein field equation, as well as many modern cosmological subjects: from primordial inflation, cosmic microwave anisotropy to the dark energy that propels an accelerating universe. The subjects are presented with an emphasis on physical examples and simple applications. One first learns how to describe curved spacetime. At this mathematically more accessible level, the reader can already study the many interesting phenomena such as gravitational lensing, black holes, and cosmology. The full tensor formulation is presented later, when the Einstein equation is solved for a few symmetric cases. Mathematical accessibility, together with the various pedagogical devices (e.g., worked-out solutions of chapter-end problems), make it practical for interested readers to use the book to study general relativity and cosmology on their own. In this new edition of the book, presentations on special relativity and black holes are augmented by new chapters. Other parts of the book are updated to include new observation tests of general relativity (e.g., the double pular system) and more recent evidence for dark matter and dark energy.Less
Einstein's general theory of relativity is introduced in this advanced undergraduate and beginning graduate level textbook. Topics include special relativity, the principle of equivalence, Riemannian geometry and tensor analysis, Einstein field equation, as well as many modern cosmological subjects: from primordial inflation, cosmic microwave anisotropy to the dark energy that propels an accelerating universe. The subjects are presented with an emphasis on physical examples and simple applications. One first learns how to describe curved spacetime. At this mathematically more accessible level, the reader can already study the many interesting phenomena such as gravitational lensing, black holes, and cosmology. The full tensor formulation is presented later, when the Einstein equation is solved for a few symmetric cases. Mathematical accessibility, together with the various pedagogical devices (e.g., worked-out solutions of chapter-end problems), make it practical for interested readers to use the book to study general relativity and cosmology on their own. In this new edition of the book, presentations on special relativity and black holes are augmented by new chapters. Other parts of the book are updated to include new observation tests of general relativity (e.g., the double pular system) and more recent evidence for dark matter and dark energy.
Steven E. Vigdor
- Published in print:
- 2018
- Published Online:
- March 2018
- ISBN:
- 9780198814825
- eISBN:
- 9780191852954
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198814825.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
Chapter 6 deals with the remaining mysteries in cosmology—dark matter, dark energy, and inflationary expansion—and the experiments aimed at solving them. It reviews the evidence for dark matter, and ...
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Chapter 6 deals with the remaining mysteries in cosmology—dark matter, dark energy, and inflationary expansion—and the experiments aimed at solving them. It reviews the evidence for dark matter, and experiments to detect the microscopic particles proposed as its constituents: weakly interacting massive particles and invisible axions. Contrasts are drawn between the failure to understand the scale of dark energy theoretically and the ambitious new survey telescopes, such as the Large Synoptic Survey Telescope (or LSST), that aim to constrain its equation of state. The theoretical concepts and possible experimental signatures of cosmic inflation are described. Searches for possible imprints from primordial inflation-induced gravitational waves on the polarization of the cosmic microwave background (CMB polarization) are discussed in the context of the pioneering first detection by the Laser Interferometer Gravitational-Wave Observatory (or LIGO) of gravitational waves from distant black-hole mergers. Philosophical questions regarding the falsifiability of inflation are raised.Less
Chapter 6 deals with the remaining mysteries in cosmology—dark matter, dark energy, and inflationary expansion—and the experiments aimed at solving them. It reviews the evidence for dark matter, and experiments to detect the microscopic particles proposed as its constituents: weakly interacting massive particles and invisible axions. Contrasts are drawn between the failure to understand the scale of dark energy theoretically and the ambitious new survey telescopes, such as the Large Synoptic Survey Telescope (or LSST), that aim to constrain its equation of state. The theoretical concepts and possible experimental signatures of cosmic inflation are described. Searches for possible imprints from primordial inflation-induced gravitational waves on the polarization of the cosmic microwave background (CMB polarization) are discussed in the context of the pioneering first detection by the Laser Interferometer Gravitational-Wave Observatory (or LIGO) of gravitational waves from distant black-hole mergers. Philosophical questions regarding the falsifiability of inflation are raised.
