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The Wave Equation inside Black Holes

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Black holes spacetimes are solutions to Einstein’s equations of general relativity that contain a black hole region, “a region of no escape”. The aim of this talk is to discuss recent developments towards understanding the dynamics of the black hole region in the context of the Cauchy problem for Einstein’s equations. In particular, I will discuss the analysis of the wave equation on Reissner–Nordström geometries, spacetimes that describe charged black holes, as a toy model for Einstein’s equations. I will highlight how the analysis in “critical” Reissner–Nordström solutions, the so-called extremal limits of Reissner–Nordström, in which the charge attains its maximal value, suggests instability outside the black hole, yet more stability inside the black hole.

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

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