Book contents
- Frontmatter
- Contents
- Preface
- 1 Preliminaries
- 2 Spacetimes admitting Killing fields
- 3 Circular spacetimes
- 4 The Kerr metric
- 5 Electrovac spacetimes with Killing fields
- 6 Stationary black holes
- 7 The four laws of black hole physics
- 8 Integrability and divergence identities
- 9 Uniqueness theorems for nonrotating holes
- 10 Uniqueness theorems for rotating holes
- 11 Scalar mappings
- 12 Self–gravitating harmonic mappings
- References
- Index
Preface
Published online by Cambridge University Press: 13 March 2010
- Frontmatter
- Contents
- Preface
- 1 Preliminaries
- 2 Spacetimes admitting Killing fields
- 3 Circular spacetimes
- 4 The Kerr metric
- 5 Electrovac spacetimes with Killing fields
- 6 Stationary black holes
- 7 The four laws of black hole physics
- 8 Integrability and divergence identities
- 9 Uniqueness theorems for nonrotating holes
- 10 Uniqueness theorems for rotating holes
- 11 Scalar mappings
- 12 Self–gravitating harmonic mappings
- References
- Index
Summary
In a manuscript communicated to the Royal Society by Henry Cavendish in 1783, an English scientist, Reverend John Michell, presented the idea of celestial bodies whose gravitational attraction was strong enough to prevent even light from escaping their surfaces. Both Michell and Laplace, who came up with the same concept in 1796, based their arguments on Newton's universal law of gravity and his corpuscular theory of light.
During the nineteenth century, a time when the notion of “dark stars” had fallen into oblivion, geometry experienced its fundamental revolution: Gauss and Lobachevsky had already found examples of non–Euclidean geometry, when Riemann became aware of the full consequences which arise from releasing the parallel axiom. In a famous lecture given at Göttingen University in 1854, the former student of Gauss introduced both the notion of spatial curvature and the extension of geometry to more than three dimensions.
It is these features of Riemannian geometry which, more than fifty years later, enabled Einstein to reveal the connection between the gravitational field and the metric structure of spacetime. In February 1916 - only three months after having achieved the final breakthrough in general relativity - Einstein presented, on behalf of Schwarzschild, the first exact solution of the new equations to the Prussian Academy of Sciences.
It took, however, almost half a century until the geometry of the Schwarzschild spacetime was correctly interpreted and its physical significance was fully appreciated.
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- Chapter
- Information
- Black Hole Uniqueness Theorems , pp. xi - xivPublisher: Cambridge University PressPrint publication year: 1996