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Linear stability of charged rotating black holes

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The Einstein field equations (EFE) are the fundamental equations of general relativity, the accepted theory of gravity. Perhaps the most striking prediction of general relativity is the existence of black holes – regions of spacetime where the gravitational field is so strong that nothing can escape. Black holes are believed to be abundant in the universe, forming when matter (such as a star or galaxy) undergoes gravitational collapse. Once a black hole has formed, it is expected to be stable. That is, black holes should not be sensitive to the influence of other objects and phenomena – they are the final state of the system. Providing a mathematical proof of the stability of black holes is one of the most important open problems in general relativity.

Great progress has been made by considering the (EFE) as a system of quasilinear wave equations. In my talk, I will introduce this approach to the study of general relativity, focusing on the linear stability of subextremal Kerr-Newman spacetimes. Each member of this family models a charged rotating black hole. The stability of this family of spacetimes is of special interest as it is closely related to the plausibility of the concept of a black hole. Time permitting, I will discuss my recent results in this direction.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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