Book contents
- Frontmatter
- Contents
- The scope of this text
- Preface to the second edition
- Acknowledgments
- 1 How the theory of relativity came into being (a brief historical sketch)
- Part I Elements of differential geometry
- Part II The theory of gravitation
- 12 The Einstein equations and the sources of a gravitational field
- 13 The Maxwell and Einstein–Maxwell equations and the Kaluza–Klein theory
- 14 Spherically symmetric gravitational fields of isolated objects
- 15 Relativistic hydrodynamics and thermodynamics
- 16 Relativistic cosmology I: general geometry
- 17 Relativistic cosmology II: the Robertson–Walker geometry
- 18 Relativistic cosmology III: the LemaÎtre–Tolman geometry
- 19 Relativistic cosmology IV: simple generalisations of L–T and related geometries
- 20 Relativistic cosmology V: the Szekeres geometries
- 21 The Kerr metric
- 22 Relativity enters technology: the Global Positioning System
- 23 Subjects omitted from this book
- 24 Comments to selected exercises and calculations
- References
- Index
14 - Spherically symmetric gravitational fields of isolated objects
from Part II - The theory of gravitation
Published online by Cambridge University Press: 30 May 2024
- Frontmatter
- Contents
- The scope of this text
- Preface to the second edition
- Acknowledgments
- 1 How the theory of relativity came into being (a brief historical sketch)
- Part I Elements of differential geometry
- Part II The theory of gravitation
- 12 The Einstein equations and the sources of a gravitational field
- 13 The Maxwell and Einstein–Maxwell equations and the Kaluza–Klein theory
- 14 Spherically symmetric gravitational fields of isolated objects
- 15 Relativistic hydrodynamics and thermodynamics
- 16 Relativistic cosmology I: general geometry
- 17 Relativistic cosmology II: the Robertson–Walker geometry
- 18 Relativistic cosmology III: the LemaÎtre–Tolman geometry
- 19 Relativistic cosmology IV: simple generalisations of L–T and related geometries
- 20 Relativistic cosmology V: the Szekeres geometries
- 21 The Kerr metric
- 22 Relativity enters technology: the Global Positioning System
- 23 Subjects omitted from this book
- 24 Comments to selected exercises and calculations
- References
- Index
Summary
Solutions of the Einstein and Einstein–Maxwell equations for spherically symmetric metrics (those of Schwarzschild and Reissner–Nordstr\“{o}m) are derived and discussed in detail. The equations of orbits of planets and of bending of light rays in a weak field are derived and discussed. Two methods to measure the bending of rays are presented. Properties of gravitational lenses are described. The proof (by Kruskal) that the singularity of the Schwarzschild metric at r = 2m is spurious is given. The relation of the r = 2m surface to black holes is discussed. Embedding of the Schwarzschild spacetime in a 6-dimensional flat Riemann space is presented. The maximal extension of the Reissner–Nordstr\“{o}m metric (by the method of Brill, Graves and Carter) is derived. Motion of charged and uncharged particles in the Reissner–Nordstr\“{o}m spacetime is described.
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- An Introduction to General Relativity and Cosmology , pp. 162 - 210Publisher: Cambridge University PressPrint publication year: 2024