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Almost all extremal black holes in AdS are singular

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arxiv 2210.02473 v3 pith:4GF7ZMKV submitted 2022-10-05 hep-th gr-qc

Gary T. Horowitz , Maciej Kolanowski , Jorge E. Santos This is my paper · ORCID
classification hep-thgr-qc
keywords blackholesextremalwhenalmostconstantcosmologicaldiverge
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We investigate the geometry near the horizon of a generic, four-dimensional extremal black hole. When the cosmological constant is negative, we show that (in almost all cases) tidal forces diverge as one crosses the horizon, and this singularity is stronger for larger black holes. In particular, this applies to generic nonspherical black holes, such as those satisfying inhomogeneous boundary conditions. Nevertheless, all scalar curvature invariants remain finite. Moreover, we show that nonextremal black holes have tidal forces that diverge in the extremal limit. Holographically, this singularity is reflected in anomalous scaling of the specific heat with temperature. Similar (albeit weaker) effects are present when the cosmological constant is positive, but not when it vanishes.

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Cited by 6 Pith papers

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