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Almost all extremal black holes in AdS are singular

Gary T. HorowitzMaciej KolanowskiJorge E. Santos
Oct 2022
摘要
We investigate the geometry near the horizon of a generic, four-dimensionalextremal black hole. When the cosmological constant is negative, we show that(in almost all cases) tidal forces diverge as one crosses the horizon, and thissingularity is stronger for larger black holes. Nevertheless, all scalarcurvature invariants remain finite. Moreover, we show that nonextremal blackholes have tidal forces that diverge in the extremal limit. Holographically,this singularity is reflected in anomalous scaling of the specific heat withtemperature. Similar (albeit weaker) effects are present when the cosmologicalconstant is positive, but not when it vanishes.
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