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Relativity in Modern Physics$
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Nathalie Deruelle and Jean-Philippe Uzan

Print publication date: 2018

Print ISBN-13: 9780198786399

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198786399.001.0001

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The Kerr solution

The Kerr solution

Chapter:
(p.481) 8 The Kerr solution
Source:
Relativity in Modern Physics
Author(s):

Nathalie Deruelle

Jean-Philippe Uzan

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198786399.003.0048

This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals. Finally, the chapter turns to the Kerr black hole, as well as its curvature singularity, horizons, static limit, and maximal extension.

Keywords:   Kerr metric, Kerr solution, Einstein vacuum equations, black holes, spacetime, Kerr–Schild metrics, Kerr black hole

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