## Flat and Curved Space-timesThe present book explains special relativity and the basics of general relativity from a geometric viewpoint. Space-time geometry is emphasized throughout, and provides the basis of understanding of the special relativity effects of time dilation, length contraction, and the relativity of simultaneity. Bondi's K-calculus is introduced as a simple means of calculating the magnitudes of these effects, and leads to a derivation of the Lorentz transformation as a way of unifying these results. The invariant interval of flat space-time is generalised to that of curved space-times, and leads to an understanding of the basic properties of simple cosmological models and of the collapse of a star to form a black hole. The appendices enable the advanced student to master the application of four-tensors to the relativistic study of energy and momentum, and of electromagnetism. In addition, this new edition contains up-to-date information on black holes, gravitational collapse, and cosmology. |

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### Contents

Introduction | 1 |

Fundamentals of measurement | 35 |

i | 44 |

The Lorentz transformation and the invariant interval | 122 |

Curved spacetimes | 196 |

Spherical and stellar collapse | 237 |

Finale | 313 |

B Fourvectors and relativistic dynamics | 325 |

Fourvectors electromagnetism and energy | 331 |

368 | |

370 | |

374 | |

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acceleration angle black holes calculation causal clock components conservation consider constant coordinate system cosmology curvature curved space-time defined detector determine direction drš Earth effect Einstein's electric field electromagnetic emitted energy equations example Exercise flat space-time four-dimensional four-momentum four-vector four-velocity frame F galaxies geodesic given gravitational field gravitational waves images inertial interval invariant inverse K-factor light cone light rays light travel Lorentz transformation magnetic field matter Maxwell's equations measured metric form metric tensor Minkowski coordinates momentum moving object obtain parallel transport particle horizon past light cone path photons physical position properties quantity quantum radar radiation redshift reference frame relation relative motion relativistic relativity theory represent rest frame rest mass result rocket rotation Section shows signals space space-time diagram special relativity speed of light star stationary Suppose surfaces of simultaneity time-like twin paradox universe model vector velocity world-line x-direction zero