## Tensor Calculus, Relativity, and Cosmology: A First CourseThis book combines relativity, astrophysics, and cosmology in a single volume, providing an introduction to each subject that enables students to understand more detailed treatises as well as the current literature. The section on general relativity gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes, Penrose processes, and similar topics), and considers the energy-momentum tensor for various solutions. The next section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects. Lastly, the section on cosmology discusses various cosmological models, observational tests, and scenarios for the early universe. * Clearly combines relativity, astrophysics, and cosmology in a single volume so students can understand more detailed treatises and current literature * Extensive introductions to each section are followed by relevant examples and numerous exercises * Provides an easy-to-understand approach to this advanced field of mathematics and modern physics by providing highly detailed derivations of all equations and results |

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#### All the Math You Need for GR

User Review - akiranick - Overstock.comIn a remarkably clear and concise manner this book manages to introduce the notations that are commonly used demonstrate how a physical system can be represented using the new formalisms outline the ... Read full review

### Contents

Introduction | 1 |

Vector Spaces | 15 |

Definitions of Tensors | 23 |

Relative Tensors | 33 |

The Metric Tensor | 43 |

Tensors as Linear Operators | 55 |

Tensor Derivatives | 61 |

ChristofFel Symbols | 71 |

Electromagnetic Fields | 135 |

Electromagnetic Field Equations | 147 |

Gravitational Fields | 165 |

Gravitational Field Equations | 177 |

Solutions of Field Equations | 193 |

Applications of the Schwarzschild Metric | 207 |

The RobertsonWalker Metric | 225 |

Cosmic Dynamics | 239 |

Differential Operators | 79 |

Geodesic Lines | 89 |

The Curvature Tensor | 97 |

Relativistic Kinematics | 111 |

Relativistic Dynamics | 123 |

Nonstatic Models of the Universe | 253 |

Quantum Cosmology | 265 |

275 | |

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### Common terms and phrases

5-symbol action integral antisymmetric black hole calculate called chapter Christoffel symbols components contravariant tensor contravariant vector coordinate system coordinates xk cosmic cosmology covariant derivative covariant vector curve definition denoted Descartes coordinates ds ds dummy indices electromagnetic field tensor element energy-momentum tensor equal to zero Euclidean metric space expression follows four-vector four-velocity free particle Friedmann equations function galaxy Gauss theorem given gravitational field equations inertial system infinitesimally invariant with respect Lagrangian density linear lower indices matrix form metric space metric tensor metric tensor gkn momentum Newtonian nonrelativistic notation obtain orthogonal pseudo-Euclidean quantity relative tensors result Ricci tensor right-hand side Robertson-Walker metric scale radius R(t Schwarzschild second kind second-order covariant tensor side of Equation sin2 solution spatial spherical coordinates Substituting symmetric system of coordinates system of reference theory of relativity three dimensions transformation law transformed according universe velocity write