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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


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