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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 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)