This page was last modified on July 1, 1998.
The second edition of Beem, Ehrlich, Easley, ``Global Lorentzian Geometry,''has been published as Volume 202 in the Marcel Dekker Pure and Applied Mathematics Series. Here is the table of contents:
Chapter 1. Introduction: Riemannian Themes in Lorentzian Geometry
Chapter 2: Connections and Curvature
2.1 Connections
2.2 Semi-Riemannian Manifolds
2.3 Null Cones and Semi-Riemannian Metrics
2.4 Sectional Curvature
2.5 The Generic Condition
2.6 The Einstein Equations
Chapter 3: Lorentzian Manifolds and Causality
3.1 Lorentzian Manifolds and Convex Normal Neighborhoods
3.2 Causality Theory of Space-times
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3.3 Limit Curves and the C Topology on Curves
3.4 Two-Dimensional Space-times
3.5 The Second Fundamental Form
3.6 Warped Products
3.7 Semi-Riemannian Local Warped Product Splittings
Chapter 4: Lorentzian Distance
4.1 Basic Concepts and Definitions
4.2 Distance-Preserving and Homothetic Maps
4.3 The Lorentzian Distance Function and Causality
4.4 Maximal Geodesic Segments and Local Causality
Chapter 5: Examples of Space-times
5.1 Minkowski Space-time
5.2 Schwarzschild and Kerr Space-times
5.3 Spaces of Constant Curvature
5.4 Robertson-Walker Space-times
5.5 Bi-invariant Lorentzian Metrics on Lie Groups
Chapter 6: Completeness and Extendibility
6.1 Existence of Maximal Geodesic Segments
6.2 Geodesic Completeness
6.3 Metric Completeness
6.4 Ideal Boundaries
6.5 Local Extensions
6.6 Singularities
Chapter 7: Stability of Completeness and Incompleteness
7.1 Stable Properties in Lor(M) and Con(M)
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7.2 The C Topology and Geodesic Systems
7.3 Stability of Geodesic Incompleteness for
Robertson-Walker Space-times
7.4 Sufficient Conditions for Stability
Chapter 8: Maximal Geodesics and Causally Disconnected Space-times
8.1 Almost Maximal Curves and Maximal Geodesics
8.2 Nonspacelike Geodesic Rays in Strongly Causal Space-times
8.3 Causally Disconnected Space-times and Nonspacelike Geodesic Lines
Chapter 9: The Lorentzian Cut Locus
9.1 The Timelike Cut Locus
9.2 The Null Cut Locus
9.3 The Nonspacelike Cut Locus
9.4 The Nonspacelike Cut Locus Revisited
Chapter 10: Morse Index Theory on Lorentzian Manifolds
10.1 The Timelike Morse Index Theory
10.2 The Timelike Path Space of a Globally Hyperbolic Space-time
10.3 The Null Morse Index Theory
Chapter 11: Some Results in Global Lorentzian Geometry
11.1 The Timelike Diameter
11.2 Lorentzian Comparison Theorems
11.3 Lorentzian Hadamard-Cartan Theorems
Chapter 12: Singularities
12.1 Jacobi Tensors
12.2 The Generic and Timelike Convergence Conditions
12.3 Focal Points
12.4 The Existence of Singularities
12.5 Smooth Boundaries
Chapter 13: Gravitational Plane Wave Space-times
13.1 The Metric, Geodesics, Curvature
13.2 Astigmatic Conjugacy and the Nonspacelike Cut Locus
13.3 Astigmatic Conjugacy and the Achronal Boundary
Chapter 14: The Lorentzian Splitting Problem in Global Lorentzian Geometry
14.1 The Busemann Function of a Timelike Geodesic Ray
14.2 Co-rays and the Busemann Function
14.3 The Level Sets of the Busemann Function
14.4 The Proof of the Lorentzian Splitting Theorem
14.5 Rigidity of Geodesic Incompleteness
Appendixes
A Jacobi Fields and Topongov's Theorem for Lorentzian Manifolds
by Steven G. Harris
B. From the Jacobi, to a Riccati, to the Raychaudhuri Equation:
Jacobi Tensor Fields and the Exponential Map Revisited