Abstract
A derivation of the Schwarzschild metric and a discussion of its main properties (including a detailed computation of the precession of the planetary orbits). The Schwarzschild solution is also used as a simple example of “black hole” geometry, in order to illustrate the physical effects of the event horizon and the need for introducing the so-called “maximal analytical extension” of the coordinate system.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Actually, radiation can be emitted thanks to quantum effects, as first shown by [24].
- 2.
There is a curious coincidence concerning the name of the physicist who discovered this metric: Schwarzschild, in German language, means indeed “black shield”.
- 3.
If the metric is not Ricci-flat, i.e. if \(R_{\mu\nu }\not=0\) and R≠0, the number of such scalar objects raises from 4 to 14.
References
Beckenstein, J.D.: Phys. Rev. D 7, 2333 (1973)
Hawking, S.W.: Commun. Math. Phys. 43, 199 (1975)
Hawking, S.W., Ellis, G.R.F.: The Large Scale Structure of Spacetime. University Press, Cambridge (1973)
Ohanian, H.C., Ruffini, R.: Gravitation and Spacetime. Norton, New York (1994)
Wald, R.: General Relativity. University of Chicago Press, Chicago (1984)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Italia
About this chapter
Cite this chapter
Gasperini, M. (2013). The Schwarzschild Solution. In: Theory of Gravitational Interactions. Undergraduate Lecture Notes in Physics. Springer, Milano. https://doi.org/10.1007/978-88-470-2691-9_10
Download citation
DOI: https://doi.org/10.1007/978-88-470-2691-9_10
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2690-2
Online ISBN: 978-88-470-2691-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)