Kerr Metric

In physics, the Kerr metric describes the geometry of spacetime around a rotating black hole. It is a metric, discovered in 1963, which is an exact solution to the Einstein field equations. The Boyer-Lindquist form of the line element is given by
ds^2=\rho^2(\frac{dr^2}{\Delta}+d\theta^2)+(r^2+a^2)\sin^2\theta d\phi^2-dt^2+\frac{2mr}{\rho^2}(a\sin^2\theta d\phi-dt)^2
where
ρ2=r2 + a2cos2θ
and
Δ=r2 - 2mr + a2.
Here m is the mass of the black hole, and a is the angular velocity, as measured by a distant observer. Note that r does not agree with the radial coordinate of the Schwarzschild solution, except asymptotically. The Kerr metric is not the most general cylindrically symmetric metric. It is the case for certain vanishing multipole moments.

References

  • Ronald Adler, Maurice Bazin, Menahem Schiffer, Introductin to General Relativity (Second Edition), (1975) McGraw-Hill New York, ISBN 0-07-000423-4 See chapter 7.

 

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