The geometry of Kerr black holes

This book offers an up-to-date look at black holes from a mathematical perspective containing many results never before published. It can be read as a broadly based introduction to modern techniques in differential geometry. Ch. 1. Background. 1.1. Manifolds. 1.2. Tensors. 1.3. Differential Geometry. 1.4. Extending Manifolds. 1.5. Lorentz Vector Spaces. 1.6. Introduction To General Relativity. 1.7. Submanifolds. 1.8. Cartan Computations -- Ch. 2. Beginning Kerr Spacetime. 2.1. The Kerr Metric. 2.2. Boyer-lindquist Blocks. 2.3. Special Submanifolds. 2.4. Ergosphere And Time Machine. 2.5. Kerr-star Spacetime. 2.6. Connection Forms. 2.7. Kerr Curvature A La Cartan -- Ch. 3. Maximal Extensions. 3.1. Star-kerr Spacetime. 3.2. Maximal Extreme Kerr Spacetime. 3.3. Extending Slow Kerr Spacetime. 3.4. Building The Crossing Spheres. 3.5. Maximal Slow Kerr Spacetime. 3.6. Bundle Structure Of Kerr Spacetime. 3.7. Isometries Of Boyer-lindquist Blocks. 3.8. Isometries Of M[subscript E] And M[subscript S]. 3.9. Topology Of Kerr Spacetime. 3.10. Kerr Chronology -- Ch. 4. Kerr Geodesics. 4.1. First-integrals. 4.2. Carter Constant. 4.3. Equations And Extensions. 4.4. Crossing Horizons. Barrett O'neill. Includes Bibliographical References (p. [367]-370) And Index. Aimed at scientists and mathematicians, this book offers an up-to-date look at the black hole from a mathematical perspective - providing results on matters such as, the determination of the isometry groups and some specific analysis of geodesic orbits.