Stability of the Kerr–Newman black hole under small perturbations

[zhumataidana22]

TL;DR

Question about the stability condition M² ≥ a² + Q² and how small perturbations affect the event horizon.

Hello everyone,

I am a Master’s student in theoretical physics currently studying the Kerr–Newman black hole solution.

I would like to better understand the stability condition

M² ≥ a² + Q².

My question is the following:

If small electromagnetic perturbations are introduced, does the event horizon remain stable?
Can such perturbations modify the horizon structure or potentially lead to instabilities?

I would also appreciate recommendations for review papers or textbooks that discuss this problem in a mathematically rigorous way.

Thank you in advance.

 

[abilkasymbalzhan]

For a non-extremal Kerr–Newman black hole satisfying M^2>a^2+Q^2, small electromagnetic (or gravitational) perturbations do not destroy the event horizon or violate the inequality; instead, they excite quasi-normal modes that decay in time, and the spacetime relaxes to a nearby Kerr–Newman solution with slightly shifted M,a,Q. Superradiance can amplify some modes, but in asymptotically flat spacetime this energy escapes to infinity, so no true instability develops. Only in special or extremal cases does the behavior become subtle, but under realistic small perturbations the horizon remains stable.

 

[berkeman]

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