## Einstein's General Theory of Relativity: With Modern Applications in CosmologyThis book introduces the general theory of relativity and includes applications to cosmology. The book provides a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, the authors offer a thorough presentation of the theory of relativity. Also included are some advanced topics not previously covered by textbooks, including Kaluza-Klein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will benefit from an updated introduction to general relativity including the most recent developments in cosmology. |

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### Contents

Problems | 17 |

Chapter 2 | 21 |

T 49 | 37 |

GENERAL THEORY OF RELATIVITY | 48 |

Chapter 3 | 54 |

4 | 63 |

Problems | 84 |

Chapter 5 | 89 |

11Gravitationalcollapse | 301 |

Universe Models with Vacuum Energy | 304 |

Problems | 359 |

AnisotropicandInhomogeneousUniverseModels | 367 |

Chapter 13 | 379 |

Problems | 383 |

Problems | 433 |

The Metric Junction Method 16 1 The relativistic theory of surface layers 439 | 441 |

6 | 109 |

151 | 150 |

Chapter 7 | 161 |

III | 179 |

Problems | 192 |

Chapter 9 | 195 |

The Schwarzschild Solution and Black Holes | 215 |

Chapter 10 | 256 |

Homogeneous and Isotropic Universe Models | 267 |

Chapter 11 | 276 |

Chapter 16 | 450 |

Braneworlds | 452 |

Chapter 18 | 478 |

KaluzaKleinTheory | 481 |

A | 503 |

D | 517 |

523 | |

533 | |