## 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 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 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

*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