## Flat and Curved Space-timesThe present book explains special relativity and the basics of general relativity from a geometric viewpoint. Space-time geometry is emphasised 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 l | 1 |

Fundamentals of measurement | 35 |

Measurements in flat spacetimes | 49 |

Copyright | |

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### Common terms and phrases

acceleration angle AT-factor black hole causal centre clock components conservation consider constant coordinate system cosmology curvature curved space-times defined density determine dilation direction discussed displacement Earth effect Einstein's electromagnetic energy equations event horizon event Q example Exercise factor flat space-time four-dimensional four-momentum four-vector four-velocity frame F fundamental observers galaxies geodesic given gravitational field gravitational waves images initial interval invariant length contraction light cone light rays light travel Lorentz transformation magnetic field matter metric form metric tensor momentum Newtonian theory object observer moving parallel parallel transport particle horizon past light cone path photograph photons physical position quantity radar radiation received redshift reference frame relation relative motion relativistic relativity theory represent rest frame rest mass result rocket rotation Section shows signals singularity space-time diagram spatial distance special relativity speed of light star stationary Suppose surfaces of simultaneity time-like twin paradox universe model vector world-line zero