Flat and Curved Space-Times

by Ellis, George F. R.; Williams, R. M.; Carfora, Mauro

• ISBN13: 9780198506577
• ISBN10: 0198506570
• Edition: 2nd
• Format: Hardcover
• Copyright: 2001-01-11
• Publisher: Oxford University Press

Summary

The 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.

Table of Contents

Introduction	1	(4)
Space--time diagrams and the foundations of special relativity	5	(30)
The concept of a space--time	5	(7)
Causality and the speed of light	12	(12)
Relative motion in special relativity	24	(11)
Fundamentals of measurement	35	(14)
Time	35	(2)
Distance	37	(4)
Simultaneity	41	(3)
World maps, world pictures, and radar maps	44	(5)
Measurements in flat space--times	49	(73)
The Doppler effect	49	(10)
Relative velocity	59	(11)
Simultaneity	70	(6)
Time dilation	76	(12)
Length contraction	88	(8)
The whole package of kinematic effects	96	(6)
Relativistic dynamics	102	(18)
The consistency of physics	120	(2)
The Lorentz transformation and the invariant interval	122	(64)
The Lorentz transformation	122	(17)
Space--time separation invariants	139	(23)
Some flat-space universes	162	(24)
Curved space--times	186	(54)
The general concept	186	(3)
Acceleration and gravitation: the principle of equivalence	189	(6)
Freely falling motion and the meaning of geodesics	195	(6)
The metric form and the metric tensor	201	(5)
The field equations	206	(3)
Light rays	209	(8)
Causality	217	(2)
Parallel propagation along a curve	219	(3)
Further tests of Einstein's theory	222	(4)
Gravitational waves	226	(3)
Detection of gravitational waves	229	(3)
Alternative theories and approaches	232	(8)
Spherical and stellar collapse	240	(24)
The Schwarzschild solution	240	(9)
Spherical collapse to black holes	249	(6)
More general black holes	255	(2)
Black hole evaporation and thermodynamics	257	(3)
Black hole candidates and ways of detecting them	260	(4)
Simple cosmological models	264	(49)
Space--time geometry	264	(7)
The evolution of the universe	271	(6)
Observable quantities	277	(7)
New observational data	284	(9)
The light cone, observational limits, and horizons	293	(8)
Steady-state and inflationary universes	301	(4)
Small universes	305	(3)
Alternative universes	308	(3)
Observational tests	311	(2)
Finale	313	(2)
Afterword	315	(53)
Appendices
A. Line integrals	318	(7)
B. Four-vectors and relativistic dynamics	325	(16)
C. Four-vectors, electromagnetism, and energy-momentum conservation	341	(27)
Symbols used	368	(1)
Index	369