## Introduction to Black Hole PhysicsThis book is about black holes, one of the most intriguing objects of modern Theoretical Physics and Astrophysics. For many years, black holes have been considered as interesting solutions of the theory of General Relativity with a number of amusing mathematical properties. Now after the discovery of astrophysical black holes, the Einstein gravity has become an important tool for their study. This self-contained textbook combines physical, mathematical, and astrophysical aspects of black hole theory. Pedagogically presented, it contains 'standard' material on black holes as well as relatively new subjects such as the role of hidden symmetries in black hole physics, and black holes in spacetimes with large extra dimensions. The book will appeal to students and young scientists interested in the theory of black holes. |

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### Contents

Big Picture | 1 |

2 Physics in a Uniformly Accelerated Frame | 47 |

3 Riemannian Geometry | 67 |

4 Particle Motion in Curved Spacetime | 109 |

5 Einstein Equations | 127 |

6 Spherically Symmetric Black Holes | 162 |

7 Particles and Light Motion in Schwarzschild Spacetime | 185 |

8 Rotating Black Holes | 242 |

Fundamental Constants and Units | 408 |

GaussCodazzi Equations | 410 |

Conformal Transformations | 412 |

Hidden Symmetries | 414 |

Boundary Term for the EinsteinHilbert Action | 431 |

Quantum Fields | 435 |

463 | |

477 | |

### Common terms and phrases

acceleration accretion angle angular momentum astrophysical asymptotically flat binary calculations circular orbit components condition conformal Consider constant coordinates corresponding covariant curvature curved deﬁned Denote density derivative disk Einstein equations emitted energy Euclidean event horizon exist extra dimensions ﬁeld flat spacetime geodesic geometry gravitational field gravitational radius gravitational waves Green function Hawking higher-dimensional impact parameter infinity integral Kerr metric Killing tensor Killing vector Killing–Yano tensor mass matter metric Eq Minkowski spacetime motion neutron star Newtonian null ray obeys object observer obtained orthogonal particle photons problem propagation properties quantum region relation Eq result Rindler rotating black hole scalar Schwarzschild Schwarzschild metric solution space space-like spherically symmetric static static spacetime stationary stress-energy tensor supermassive black holes surface symmetry temperature theorem theory time-like topology trajectory transformation vacuum vanishes velocity wormhole