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arXiv 2210.02473hep-thgr-qc
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几乎所有AdS中的极值黑洞都是奇异的

Almost all extremal black holes in AdS are singular

Gary T. Horowitz, Maciej Kolanowski, Jorge E. Santos

摘要:

我们研究了一般四维极值黑洞视界附近的几何结构。当宇宙学常数为负时,我们证明了(几乎在所有情况下)潮汐力随着穿过视界而发散,并且这种奇异性对于较大的黑洞更强。特别是,这适用于一般的非球形黑洞,如那些满足非齐次边界条件。然而,所有标量曲率不变量仍然是有限的。此外,我们表明,非极值黑洞的潮汐力,在极值极限发散。从全息图上看,这种奇异性反映在比热随温度的反常标度上。当宇宙学常数为正值时,也会出现类似的(尽管较弱)效应,但当它为零时就不会出现。

英文摘要:

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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