Black Holes

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9781860945885 | 1860945880
Cover: Paperback
Copyright: 12/30/2005

Rent

(Recommended)

$19.47

Term

Due

Price

Semester

Aug 2

$19.47

Quarter

Jul 19

$18.50

Short Term

Jun 21

$17.52

*This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping cart.
Buy New

In Stock Usually Ships in 24 Hours

$26.60

This introduction to the fascinating subject of black holes fills a significant gap in the literature which exists between popular, non-mathematical expositions and advanced textbooks at the research level. It is designed for advanced undergraduates and first year postgraduates as a useful stepping-stone to the advanced literature. The book provides an accessible introduction to the exact solutions of Einstein's vacuum field equations describing spherical and axisymmetric (rotating) black holes. The geometry and physical properties of these spacetimes are explored through the motion of particles and light. The use of different coordinate systems, maximal extensions and Penrose diagrams is explained. The association of the surface area of a black hole with its entropy is discussed and it is shown that with the introduction of quantum mechanics black holes cease to be black and can radiate. This result allows black holes to satisfy the laws of thermodynamics and thus be consistent with

Preface

1 Relativistic Gravity

(12)

1.1 What is a black hole?

(2)

1.2 Why study black holes?

(1)

1.3 Elements of general relativity

(10)

1.3.1 The principle of equivalence

(1)

1.3.2 The Newtonian affine connection

(1)

1.3.3 Newtonian gravity

(1)

1.3.4 Metrics in relativity

(1)

1.3.5 The velocity and momentum 4-vector

(1)

1.3.6 General vectors and tensors

(1)

1.3.7 Locally measured physical properties

(1)

1.3.8 Derivatives in relativity

(2)

1.3.9 Acceleration 4-vector

(1)

1.3.10 Paths of light

(1)

1.3.11 Einstein's field equations

(1)

1.3.12 Symmetry and Killing's equation

(2)

2 Spherical Black Holes

(44)

2.1 The Schwarzschild metric

(5)

2.1.1 Coordinates

(1)

2.1.2 Proper distance

(1)

2.1.3 Proper time

(1)

2.1.4 Redshift

(1)

2.1.5 Interpretation of M and geometric units

(1)

2.1.6 The Schwarzschild radius

(1)

2.1.7 The event horizon

(1)

2.1.8 Birkoff's theorem

(1)

2.1.9 Israel's theorem

(1)

2.2 Orbits in Newtonian gravity

(1)

2.2.1 Energy

(1)

2.2.2 Angular momentum

(1)

2.2.3 The Newtonian effective potential

(1)

2.2.4 Classification of Newtonian orbits

(1)

2.3 Particle orbits in the Schwarzschild metric

(9)

2.3.1 Constants of the motion

(1)

2.3.2 Energy

(1)

2.3.3 Angular momentum

(1)

2.3.4 The effective potential

(1)

2.3.5 Newtonian approximation to the metric

(1)

2.3.6 Classification of orbits

(1)

2.3.7 Radial infall

(1)

2.3.8 The locally measured energy of a particle

(1)

2.3.9 Circular orbits

(1)

2.3.10 Comparison with Newtonian orbits

(1)

2.3.11 Orbital velocity in the frame of a hovering observer

(1)

2.3.12 Energy in the last stable orbit

(1)

2.4 Orbits of light rays

(3)

2.4.1 Radial propagation of light

(1)

2.4.2 Capture cross-section for light

(1)

2.4.3 The view of the sky for a stationary observer

(1)

2.5 Classical tests

(1)

2.6 Falling into a black hole

(4)

2.6.1 Free-fall time for a distant observer

(2)

2.6.2 Light-travel time

(1)

2.6.3 What the external observer sees

(1)

2.6.4 An infalling observer's time

(1)

2.6.5 What the infalling observer feels

(1)

2.7 Capture by a black hole

(2)

2.7.1 Case I: Capture of high angular momentum particles

(1)

2.7.2 Case II: Capture of low energy particles

(1)

2.8 Surface gravity of a black hole

(3)

2.8.1 The proper acceleration of a hovering observer

(1)

2.8.2 Surface gravity

(1)

2.8.3 Rindler coordinates

(2)

2.9 Other coordinates

(2)

2.9.1 Null coordinates

(1)

2.9.2 Eddington—Finkelstein coordinates

(1)

2.10 Inside the black hole

(2)

2.10.1 The infalling observer

(1)

2.11 White holes

(1)

2.12 Kruskal coordinates

(3)

2.12.1 The singularities at r = 0 and cosmic censorship

(1)

2.12.2 The spacetime of a collapsing star

(1)

2.13 Embedding diagrams

(2)

2.14 Asymptotic flatness

(2)

2.14.1 The Penrose–Carter diagram for the Schwarzschild metric

(1)

2.14.2 The Penrose–Carter diagram for the Newtonian metric

(1)

2.15 Non-isolated black holes

(2)

2.15.1 The infinite redshift surface

(1)

2.15.2 Trapped surfaces

(1)

2.15.3 Apparent horizon

(1)

2.16 The membrane paradigm

(2)

3 Rotating Black Holes

(46)

3.1 The Kerr metric

(1)

3.2 The event horizon

(2)

3.2.1 The circumference of the event horizon

(1)

3.2.2 The area of the event horizon

(1)

3.3 Properties of the Kerr metric coefficients

(1)

3.3.1 Identities

(1)

3.3.2 Contravariant components

(1)

3.4 Interpretation of m, a and geometric units

(1)

3.5 Extreme Kerr black hole

(1)

3.6 Robinson's theorem

(1)

3.7 Particle orbits in the Kerr geometry

(4)

3.7.1 Constants of the motion

(1)

3.7.2 Energy

(1)

3.7.3 Angular momentum

(1)

3.7.4 The Carter integral

(1)

3.7.5 The radial equation

(1)

3.7.6 The effective potential

(1)

3.8 Frame-dragging

(3)

3.8.1 Orbits of zero angular momentum particles

(1)

3.8.2 Orbits with non-zero angular momentum

(1)

3.9 Zero angular momentum observers (ZAMOs)

(3)

3.9.1 Some applications of ZAMOs

(2)

3.10 Photon orbits

(2)

3.10.1 The photon effective potential

(1)

3.10.2 Azimuthal motion

(1)

3.10.3 Photon capture cross-section

(1)

3.11 The static limit surface

(2)

3.12 The infinite redshift surface

(1)

3.13 Circular orbits in the equatorial plane

(6)

3.13.1 Innermost (marginally) stable circular orbit

(2)

3.13.2 Period of a circular orbit

(1)

3.13.3 Energy of the innermost stable orbit

(1)

3.13.4 Angular momentum of the innermost stable orbit

(1)

3.13.5 Marginally bound orbits

(1)

3.13.6 Unbound orbits

(1)

3.14 Polar orbits

(3)

3.14.1 Orbital period

(1)

3.15 The ergosphere

(4)

3.15.1 Negative energy orbits

(1)

3.15.2 Angular momentum of a negative energy particle

(1)

3.15.3 The Penrose process

(1)

3.15.4 Realising the Penrose process

(2)

3.16 Spinning up a black hole

(3)

3.16.1 From Schwarzschild to extreme Kerr black hole

(1)

3.17 Other coordinates

(1)

3.18 Penrose-Carter diagram

(4)

3.18.1 Interior solutions and collapsing stars

(1)

3.19 Closed timelike lines

(1)

3.20 Charged black holes

(5)

4 Black Hole Thermodynamics

103

(34)

4.1 Black hole mechanics

103

(4)

4.1.1 Surface gravity

103

(2)

4.1.2 Redshift

105

(1)

4.1.3 Conservation of energy

106

(1)

4.2 The area of a Kerr black hole horizon cannot decrease

107

(3)

4.2.1 Area change by accretion

107

(1)

4.2.2 Area change produced by the Penrose process

108

(1)

4.2.3 The area theorem

109

(1)

4.2.4 Irreducible mass

109

(1)

4.2.5 Maximum energy extraction

109

(1)

4.2.6 Naked singularities

110

(1)

4.3 Scattering of waves

110

(6)

4.3.1 Superradiance

110

(6)

4.4 Thermodynamics

116

(5)

4.4.1 Horizon temperature

118

(2)

4.4.2 The four laws of black hole thermodynamics

120

(1)

4.5 Hawking radiation

121

(10)

4.5.1 Introduction

121

(1)

4.5.2 Casimir effect

122

(1)

4.5.3 Thermal vacua in accelerated frames

122

(5)

4.5.4 Hawking radiation

127

(4)

4.6 Properties of radiating black holes

131

(3)

4.6.1 Entropy and temperature

131

(1)

4.6.2 Radiating black holes

132

(1)

4.6.3 Black hole in a box

133

(1)

4.7 Entropy and microstates

134

(3)

5 Astrophysical Black Holes

137

(10)

5.1 Introduction

137

(1)

5.2 Stellar mass black holes

138

(4)

5.2.1 Formation

138

(2)

5.2.2 Finding stellar mass black holes

140

(1)

5.2.3 The black hole at the centre of the Galaxy

141

(1)

5.3 Supermassive black holes in other galaxies

142

(3)

5.3.1 Intermediate mass black holes

143

(1)

5.3.2 Mini black holes

144

(1)

5.4 Further evidence for black hole spin

145

(1)

5.5 Conclusions

146

(1)

References

147

(4)

Bibliography

151

(2)

Index

153

Please wait while the item is added to your bag...

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Black Holes

Summary

Table of Contents

Supplemental Materials