## Black Hole Spin

*Charles D. Bailyn*

### in What Does a Black Hole Look Like?

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691148823
- eISBN:
- 9781400850563
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691148823.003.0008
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter examines the spin of a black hole. The spin is usually described as a nondimensional parameter, which can range from zero (a nonspinning black hole) to one (a situation described as ... More

## Spherically symmetric spacetime — GR tests

*Ta-Pei Cheng*

### in Relativity, Gravitation and Cosmology: A Basic Introduction

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199573639
- eISBN:
- 9780191722448
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573639.003.0007
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

A spherically symmetric metric has two unknown scalar metric functions. The Schwarzschild solution to the GR field equation is presented. An embedding diagram is used to visualize such a warp space. ... More

## GR as a geometric theory of gravity — II

*Ta-Pei Cheng*

### in Relativity, Gravitation and Cosmology: A Basic Introduction

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199573639
- eISBN:
- 9780191722448
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573639.003.0014
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

The mathematical realization of equivalence principle (EP) is the principle of general covariance. General relativity (GR) equations must be covariant with respect to general coordinate ... More

## Spherically Symmetric Black Holes

*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/9780199692293.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

To derive spherically symmetric solutions of the Einstein equations the dimensional reduction is used. The Birkhoff theorem is proved, which shows that any vacuum spherically symmetric solution ... More

## A College Course on Relativity and Cosmology

*Ta-Pei Cheng*

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199693405
- eISBN:
- 9780191803130
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199693405.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This book introduces Einstein’s general theory of relativity. Topics include the geometric formulation of special relativity, the principle of equivalence, the Einstein field equation and its ... More

## “Cruel and Unusual Punishment”?

*Scott Christianson*

### in The Last Gasp: The Rise and Fall of the American Gas Chamber

- Published in print:
- 2010
- Published Online:
- March 2012
- ISBN:
- 9780520255623
- eISBN:
- 9780520945616
- Item type:
- chapter

- Publisher:
- University of California Press
- DOI:
- 10.1525/california/9780520255623.003.0012
- Subject:
- History, American History: 20th Century

By the late 1970s, public opinion in the United States was swinging ever more strongly in favor of the death penalty. Although the public's appetite for gas chambers had diminished, eleven ... More

## The Schwarzschild black hole

*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/9780198786399.003.0047
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses the Schwarzschild black hole. It demonstrates how, by a judicious change of coordinates, it is possible to eliminate the singularity of the Schwarzschild metric and reveal a ... More

## The Cartan structure 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/9780198786399.003.0065
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter focuses on Cartan structure equations. It first introduces a 1-form and its exterior derivative, before turning to a study of the connection and torsion forms, thereby expressing the ... 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

## The Schwarzschild solution

*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/9780198786399.003.0046
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter deals with the Schwarzschild metric. To find the gravitational potential U produced by a spherically symmetric object in the Newtonian theory, it is necessary to solve the Poisson ... More

## Equations of motion

### in Advanced General Relativity: Gravity Waves, Spinning Particles, and Black Holes

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199680696
- eISBN:
- 9780191760662
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199680696.003.0003
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

A technique for extracting the relativistic equations of motion of Schwarzschild, Reissner–Nordström, or Kerr particles moving in external fields, from the vacuum Einstein or Einstein–Maxwell field ... More

## The Einstein field equation

*Ta-Pei Cheng*

### in Einstein's Physics: Atoms, Quanta, and Relativity - Derived, Explained, and Appraised

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199669912
- eISBN:
- 9780191744488
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199669912.003.0014
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

Newton’s 1/ r 2 gravitational force law is finally explained. The ... More

## General Relativity

*Nicholas Manton and Nicholas Mee*

### in The Physical World: An Inspirational Tour of Fundamental Physics

- 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 ... More

## Schwarzschild’s Spacetime

*Prasenjit Saha and Paul A. Taylor*

### in The Astronomers' Magic Envelope: An Introduction to Astrophysics Emphasizing General Principles and Orders of Magnitude

- Published in print:
- 2018
- Published Online:
- July 2018
- ISBN:
- 9780198816461
- eISBN:
- 9780191858246
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198816461.003.0003
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

The concept of a metric is motivated and introduced, along with the introduction of relativistic quantities of spacetime, proper time, and Einstein’s field equations. Geodesics are cast in basic form ... More

## General relativistic time

*George Jaroszkiewicz*

### in Images of Time: Mind, Science, Reality

- Published in print:
- 2016
- Published Online:
- January 2016
- ISBN:
- 9780198718062
- eISBN:
- 9780191787553
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198718062.003.0019
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses the transition from special relativistic (Minkowski) spacetime to general relativistic spacetimes. It reviews the concept of timelike, spacelike, and null (or lightlike) vector ... More

## Black holes

*Michael Kachelriess*

### in Quantum Fields: From the Hubble to the Planck Scale

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198802877
- eISBN:
- 9780191841330
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198802877.003.0025
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

Black holes are introduced as solutions of Einsteins equations contain-ing a physical singularity covered by an event horizon. The properties of Schwarzschild and of Kerr black holes are examined. It ... More

## Radiative Transfer

*Kelly Chance and Randall V. Martin*

### in Spectroscopy and Radiative Transfer of Planetary Atmospheres

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780199662104
- eISBN:
- 9780191748370
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199662104.003.0004
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics

Radiative transfer is the process of energy transfer during the propagation of electromagnetic radiation through a medium. The processes of extinction, due to absorption and scattering, and thermal ... More

## Einstein Equation and its Spherical Solution

*Ta-Pei Cheng*

### in A College Course on Relativity and Cosmology

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199693405
- eISBN:
- 9780191803130
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199693405.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

The general relativity (GR) field equation relates spacetime curvature to mass/energy distribution. Its solution is the metric, determining spacetime geometry. This chapter introduces curvature in ... More

## Black Holes

*Ta-Pei Cheng*

### in A College Course on Relativity and Cosmology

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199693405
- eISBN:
- 9780191803130
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199693405.003.0007
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

A black hole is an object that is inside its event horizon at r=r*: a one-way surface that particles and light can only traverse inward. This chapter studies the spherically symmetric nonrotating ... More

## Karl Schwarzschild: Astronomer and Physicist

*Helge Kragh*

### in Masters of the Universe: Conversations with Cosmologists of the Past

- Published in print:
- 2014
- Published Online:
- March 2015
- ISBN:
- 9780198722892
- eISBN:
- 9780191789564
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198722892.003.0003
- Subject:
- Physics, History of Physics, Particle Physics / Astrophysics / Cosmology

The German astronomer and physicist Karl Schwarzschild was interviewed in March 1916, a few months before he died after a serious illness. In this last interview he recounted his work in astronomy ... More