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General Relativity and the Einstein Equations

Yvonne Choquet-Bruhat

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199230723
eISBN:
9780191710872
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230723.001.0001
Subject:
Mathematics, Applied Mathematics

General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these ... More


Introduction to 3+1 Numerical Relativity

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 ... More


Time warps and bent space

Louis A. Girifalco

in The Universal Force: Gravity - Creator of Worlds

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199228966
eISBN:
9780191711183
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228966.003.0015
Subject:
Physics, History of Physics

General relativity is the extension of the ideas of relativity to accelerated motion. It starts with the premise that the laws of physics should be the same for all, whatever the state of motion. It ... More


The Annotated Manuscript

Hanoch Gutfreund and Jürgen Renn

in The Road to Relativity: The History and Meaning of Einstein's "The Foundation of General Relativity", Featuring the Original Manuscript of Einstein's Masterpiece

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175812
eISBN:
9781400865765
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175812.003.0003
Subject:
Physics, History of Physics

This section presents annotations of the manuscript of Albert Einstein's canonical 1916 paper on the general theory of relativity. It begins with a discussion of the foundation of the general theory ... More


GRAVITATIONAL ANOMALIES

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses chiral anomalies associated with the gravitational field, namely, gravitational anomalies. It discusses gravitational generalization of chiral U(1) anomalies for ordinary gauge ... More


The Controversy over Gravitational Waves

Hanoch Gutfreund and Jürgen Renn

in The Formative Years of Relativity: The History and Meaning of Einstein's Princeton Lectures

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 ... More


The early-type magnetic stars

Leon Mestel

in Stellar Magnetism: Second Edition

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199641741
eISBN:
9780191738609
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641741.003.0009
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Chapters 4 and 5 discussed various aspects of the interaction between the magnetic field and the thermal-gravitational-rotational fields in different stellar domains. This chapter broadens the ... More


Gravity

VOLOVIK GRIGORY E.

in The Universe in a Helium Droplet

Published in print:
2009
Published Online:
January 2010
ISBN:
9780199564842
eISBN:
9780191709906
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199564842.003.0002
Subject:
Physics, Condensed Matter Physics / Materials, Particle Physics / Astrophysics / Cosmology

This chapter discusses the Einstein theory of gravity, which consists of two main elements: (1) gravity is related to a curvature of space-time in which particles move along geodesic curves; and (2) ... More


Physics in a Uniformly Accelerated Frame

Valeri P. Frolov and Andrei Zelnikov

in Introduction to Black Hole Physics

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199692293
eISBN:
9780191731860
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199692293.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Equivalence principle relates physics in an accelerated frame and in a gravitational field. It is possible to understand many properties of black holes beginning with the flat Minkowski spacetime. We ... More


Small black holes: geometrical preliminaries

H. Asada, T. Futamase, and P. A. Hogan

in Equations of Motion in General Relativity

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199584109
eISBN:
9780191723421
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199584109.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

To model a small black hole moving in an external field we follow the approach of Futamase, Hogan, and Itoh. The space‐time model of the external field provides us with a background space‐time. If ... More


The law of gravitation

Nathalie Deruelle and Jean-Philippe Uzan

in Relativity in Modern Physics

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198786399
eISBN:
9780191828669
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198786399.003.0011
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter embarks on the study of Newton’s law of gravitation. It first discusses gravitational mass and inertial mass, a measure of the ‘resistance’ of the point particle to an applied force. The ... More


The General Theory of Relativity (Continued)

Hanoch Gutfreund and Jürgen Renn

in The Formative Years of Relativity: The History and Meaning of Einstein's Princeton Lectures

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691174631
eISBN:
9781400888689
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174631.003.0017
Subject:
Physics, History of Physics

This chapter shows that in the limit of weak fields and low velocities, the equation of the geodesic line reduces to Newton's equation of motion. It proceeds to derive the gravitational field ... More


The General Theory of Relativity

Hanoch Gutfreund and Jürgen Renn

in The Formative Years of Relativity: The History and Meaning of Einstein's Princeton Lectures

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691174631
eISBN:
9781400888689
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174631.003.0016
Subject:
Physics, History of Physics

This chapter shows how Einstein has developed and described the mathematical apparatus that is necessary to formulate the physical contents of the general theory of gravity. It first discusses the ... More


Gauge Field Theory and Gravitation

Daniel Canarutto

in Gauge Field Theory in Natural Geometric Language: A revisitation of mathematical notions of quantum physics

Published in print:
2020
Published Online:
December 2020
ISBN:
9780198861492
eISBN:
9780191894374
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198861492.003.0006
Subject:
Mathematics, Applied Mathematics, Mathematical Physics

The notion of 2-spinor soldering form allows a neat formulation, called the ‘tetrad-affine setting’, of a theory of matter and gauge fields interacting with the gravitational field. The latter is ... More


The Einstein equations

Nathalie Deruelle and Jean-Philippe Uzan

in Relativity in Modern Physics

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198786399
eISBN:
9780191828669
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198786399.003.0044
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter deals with Einstein equations. In the absence of matter there is no gravitational field, and the spacetime which represents this empty universe is Minkowski spacetime. More precisely, if ... More


The First Solutions and the Challenge of Their Interpretation

Hanoch Gutfreund and Jürgen Renn

in The Formative Years of Relativity: The History and Meaning of Einstein's Princeton Lectures

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691174631
eISBN:
9781400888689
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174631.003.0006
Subject:
Physics, History of Physics

This chapter discusses the first wave of the exploration of exact solutions to Einstein's gravitational field equations. When Einstein published the final form of the field equations in 1915, only an ... More


Tests in the solar system

Nathalie Deruelle and Jean-Philippe Uzan

in Relativity in Modern Physics

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198786399
eISBN:
9780191828669
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198786399.003.0051
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter describes observable relativistic effects in the solar system. In the solar system we can, as a first approximation, neglect the gravitational field of all the stars except the Sun. In ... More


Matter in curved spacetime

Nathalie Deruelle and Jean-Philippe Uzan

in Relativity in Modern Physics

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198786399
eISBN:
9780191828669
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198786399.003.0043
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter is concerned with the laws of motion of matter—particles, fluids, or fields—in the presence of an external gravitational field. In accordance with the equivalence principle, this motion ... More


The post-Newtonian approximation

Nathalie Deruelle and Jean-Philippe Uzan

in Relativity in Modern Physics

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198786399
eISBN:
9780191828669
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198786399.003.0052
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter embarks on a study of the two-body problem in general relativity. In other words, it seeks to describe the motion of two compact, self-gravitating bodies which are far-separated and ... More


The physics of black holes I

Nathalie Deruelle and Jean-Philippe Uzan

in Relativity in Modern Physics

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198786399
eISBN:
9780191828669
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198786399.003.0049
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter describes two physical processes related to the Schwarzschild and Kerr solutions which can be induced by the gravitational field of a black hole. The first is the Penrose process, which ... More


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