Almost all extremal black holes in AdS are singular

TL;DR

This paper demonstrates that most extremal black holes in Anti-de Sitter space exhibit horizon singularities characterized by diverging tidal forces, despite finite scalar curvature invariants, with implications for holography and black hole physics.

Contribution

It reveals that generic extremal AdS black holes have horizon tidal force singularities, extending understanding of their geometric and holographic properties.

Findings

Tidal forces diverge at the horizon for most extremal AdS black holes.

Scalar curvature invariants remain finite despite tidal force divergence.

Singularities are stronger for larger black holes and are reflected holographically in specific heat anomalies.

Abstract

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.