paper

Black Hole Singularities from Holographic Complexity

arXiv:2504.10194 · doi:10.1007/JHEP07(2025)275

Abstract

Using a second law of complexity, we prove a black hole singularity theorem. By introducing the notion of trapped extremal surfaces, we show that their existence implies null geodesic incompleteness inside globally hyperbolic black holes. We also demonstrate that the vanishing of the growth rate of the volume of extremal surfaces provides a sharp diagnostic of the black hole singularity. In static, uncharged, spherically symmetric spacetimes, this corresponds to the growth rate of spacelike extremal surfaces going to zero at the singularity. In charged or rotating spacetimes, such as the Reissner-Nordström and Kerr black holes, we identify novel timelike extremal surfaces that exhibit the same behavior at the timelike singularity.

16 pages and 5 figures. v2 : Added references and fixed minor typos. v3 : Expanded the proof, added more discussion and details in several sections, included two figures, and added additional references

References in corpus (20)