## Black Holes: The Membrane ParadigmA pedagogical introduction to the physics of black holes. The membrane paradigm represents the four-dimemnsional spacetime of the black hole's event horizon as a two-dimensional membrane in three-dimensional space, allowing the reader to understand and compute the behavior of black holes in complex astrophysical environments. |

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### Contents

Nonrotating and Slowly Rotating Holes | 13 |

The Stretched Horizon of a Nonrotating or Slowly | 27 |

Model Problems for Nonrotating and Slowly Rotating Holes | 41 |

Rapidly Rotating Holes | 67 |

B The 3+1 Split of the Laws of Physics outside a Rotating | 81 |

The Stretched Horizon of a Rotating Hole | 94 |

Astrophysical Applications of BlackHole | 121 |

Qualitative Features of the BlackHole Magnetosphere | 132 |

A Conceptual Foundations | 182 |

Structure and Evolution of the Stretched Horizon | 196 |

Summary of the laws of evolution of the stretched | 234 |

B Rotating Perturbations | 245 |

E Model Problems with Radially Moving Particles | 268 |

The Thermal Atmosphere of a Black Hole | 280 |

B The Physical Laws Governing Black Hole Atmospheres | 286 |

Model Problems for BlackHole Atmospheres | 314 |

Structure and Energetics of a Stationary Axisymmetric | 138 |

Gravitational Interaction of a Black | 146 |

B Model Problems for the Precession of Black Holes | 171 |

341 | |

Author Index | 349 |

### Common terms and phrases

3+1 split absolute space accretion disk angular momentum angular velocity astrophysical asymptotic rest frame axis black-hole charge components compute conservation coordinates correspondingly curvature curve density derived dissipation electric field electromagnetic embedding diagram entropy equation evolution external universe FIDO-measured FIDOs fiducions fluid flux gravitational acceleration gravitational fields gravitomagnetic Hartle hole's mass hole's rotation inertial frame integral interaction izon lapse function Lorentz Macdonald magnetic field magnitude membrane paradigm metric model problem modes motion and precession move neutron star Newtonian nonrotating hole orbit particle perturbations physical precession precisely produced quadrupole quanta radial radius redshifted energy region relative renormalized Rindler rotating black hole rotating hole Schwarzschild hole shear slicing spacetime spatial spin stretched horizon subsection surface tensor Teukolsky thermodynamics Thorne tidal field tidal force tidal torque tion torque true horizon unperturbed vacuum vanishes vector viewpoint viscous waves