General Relativity: A Graduate Course

Horatiu Nastase

doi:10.1017/9781009575737

This text on general relativity and its modern applications is suitable for an intensive one-semester course on general relativity, at the level of a Ph.D. student in physics. Assuming knowledge of classical mechanics and electromagnetism at an advanced undergraduate level, basic concepts are introduced quickly, with greater emphasis on their applications. Standard topics are covered, such as the Schwarzschild solution, classical tests of general relativity, gravitational waves, ADM parametrization, relativistic stars and cosmology, as well as more advanced standard topics like vielbein-spin connection formulation, trapped surfaces, the Raychaudhuri equation, energy conditions, the Petrov and Bianchi classifications and gravitational instantons. More modern topics, including black hole thermodynamics, gravitational entropy, effective field theory for gravity, the PPN expansion, the double copy and fluid-gravity correspondence, are also introduced using the language understood by physicists, without too abstract mathematics, proven theorems, or the language of pure mathematics.

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Contents

Frontmatter
pp i-iv
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Dedication
pp v-vi
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Contents
pp vii-xiv
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Preface
pp xv-xv
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Acknowledgments
pp xvi-xvi
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Introduction
pp 1-2
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1 - General relativity, kinematics: metric, parallel transport, and general coordinate invariance
pp 3-17
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2 - General relativity, dynamics: curvature, the Einstein–Hilbert action, and the Einstein equation
pp 18-32
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3 - Perturbative gravity: Fierz–Pauli action and gauge conditions
pp 33-41
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4 - Gravitational waves: perturbation, exact solutions, generation, and multipole expansion
pp 42-53
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5 - Nonperturbative gravity: the vacuum Schwarzschild solution
pp 54-63
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6 - Deflection of light by the Sun and comparison with special relativity
pp 64-74
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7 - The other classical tests of general relativity: the gravitational redshift, the perihelion precession, and the time delay of radar
pp 75-85
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8 - Vielbein–spin connection formulation of general relativity: gravity vs. gauge theory, in four dimensions and three dimensions
pp 86-95
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9 - Gravity and geometry, Lovelock and Chern–Simons, topological terms, extensions, and anomalies
pp 96-104
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10 - The ADM parametrization and applications
pp 105-115
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11* - Canonical formalism for gravity, the Wheeler–de Witt equation, and the canonical quantization of gravity
pp 116-127
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12 - Gravitoelectric and gravitomagnetic fields and applications
pp 128-136
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13 - Penrose diagrams and black holes: the Schwarzschild example
pp 137-148
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14 - Reissner–Nordstrom black hole spacetime and extremal black holes
pp 149-157
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15 - Kerr and Kerr–Newman black hole spacetimes and the Penrose process
pp 158-167
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16 - Trapped surfaces, event horizons, causality, and topology
pp 168-179
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17 - The Raychaudhuri equation
pp 180-187
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18 - The laws of black hole thermodynamics and black hole radiation
pp 188-198
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19 - Wald entropy and Sen’s entropy function formalism
pp 199-208
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20 - Energy conditions, singularity theorems, and wormholes
pp 209-218
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21 - Relativistic stars and gravitational collapse to black holes
pp 219-230
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22 - Effective field theory from gravity and black holes
pp 231-247
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23 - General relativity solutions and the gauge theory double copy
pp 248-260
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24 - The fluid–gravity correspondence
pp 261-271
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General Relativity

A Graduate Course

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