## Einstein's General Theory of Relativity: With Modern Applications in CosmologyThe book introduces the general theory of relativity and includes applications to cosmology. The book contains a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, we give a thorough presentation of the theory of relativity. Also, some advanced topics not previously covered by textbooks; e.g. 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 get 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 | |

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### Common terms and phrases

acceleration angular arbitrary assume basis vectors Bianchi type big bang black hole brane calculate Christoffel symbols clock comoving components consider coordinate system cosmic cosmological constant covariant derivative curvature curve deceleration parameter defined density differentiation dimension distance Einstein Einstein field equations electromagnetic energy-momentum tensor Euclidean Example expansion expression five-dimensional flat ﬂuid four-dimensional four-velocity Friedmann equation function geodesic geometry given gives gravitational field Hence horizon Hubble parameter hypersurfaces inertial integral invariant Killing vectors Lagrangian Lie algebra line-element Lorentz mass matrix measured metric tensor Minkowski moving Newton’s Newtonian observer one-form particle photon radiation redshift reference frame relativistic Ricci tensor Riemann tensor rotating scalar Schwarzschild radius Show sin2 singularity Sitter solution space spacetime spatial spherical surface symmetric temperature theory of relativity time-like transformation universe model vacuum energy vanishes vector field velocity written