Gravity, Black Holes, and the Very Early Universe

Preface Chapter 1 Basic Ideas of General Relativity 1.1 Inadequacy of special relativity and Mach's principle 1.2 Einstein's principle of equivalence 1.3 Immediate consequences of the principle of equivalence The bending of a light beam Gravitational shift of spectral lines 1.4 The curved spacetime concept 1.5 The principle of general covariance 1.6 Distance and time intervals References Problems Chapter 2 Curvilinear Coordinates and General Tensors 2.1 Curvilinear coordinates 2.2 Parallel displacement and covariant differentiation 2.3 Symmetry properties of the Christoffel symbols 2.4 Christoffel symbols and the metric tensor 2.5 The Geodesics 2.6 The stationary property of geodesics 2.7 The curvature tensor 2.8 Geodesic deviation 2.9 Laws of physics in curved space 2.10 The metric tensor and the classical gravitational potential 2.11 Some useful calculation aids References Problems Chapter 3 Einstein's Law of Gravitation 3-1 Introduction (summary of general principles) 3-2 A heuristic derivation of Einstein's equations 3-3 Energy-momentum tensor References Problems Chapter 4 The Schwarzschild Solution 4-1 The Schwarzschild metric 4-2 The Schwarzschild solution of the vacuum field equations The gravitational redshift 4-3 Isotropic coordinates 4-4 Schwarzschild geodesic 4-5 First integrals of the Schwarzschild solutions 4-6 Quasiuniform gravitational field References Problems Chapter 5 Experimental Tests of Einstein's Theory 5-1 Precession of the perihelion of Mercury 5-2 Deflection of light rays in a gravitational field 5-3 Light retardation (The Shaoiro experiment) 5-4 Test of gravitational radiation(Hulse-Taylor's measurement of decay of the orbit of the binary pulsar PSR-1913+16) References Problems Chapter 6 The Physics of Black Holes 6-1 The Schwarzschild black holes 6-2 Inside a black hole 6-3 How a black hole forms 6-4 The Kerr-Newmann black holes Energy extraction from a rotating black hole: the Penrose process The area theorem Energy extraction from two coalescing black holes 6-5 Thermodynamics of black holes Quantum mechanics of black holes; Hawking radiation 6-6 The detection of black holes a. Detection of stellar-mass black holes b. Supermassive black holes in the centers of galaxies c. Intermediate-mass black holes 6-7 How do electric and gravitational fields get out of black holes? 6-8 Black holes and particle Physics References Problems Chapter 7 Introduction to Cosmology 7-1 Introduction 7-2 A little history on the development of western cosmological concepts Ancient Greece The renaissance of cosmology Newton and infinite universe Newton's law pf gravity predicts a non-stationary universe Olbers's paradox 7-3 The discovery of expansion of the universe 7-4 The Big Bang Cosmological redshift 7-5 The microwave background radiation 7-6 Additional evidence for the Big Bang References Problems Chapter 8 Big Bang Models 8-1 The cosmic fluid and fundamental observers 8-2 Properties of the Robertson-Walker metric 8-3 Cosmic dynamics; Friedmann's equations 8-4 The solutions of Friedmann's equations A. Flat model (k = 0) B. Closed model (k = 1) C. Open model (k = -1) 8-5 Dark matter and the fate of the universe 8-6 The Beginning, the end, and time's arrow 8-7 An accelerating universe? 8-8 The co