Possible Resolution of Black Hole Singularities from Large N Gauge Theory

TL;DR

The paper investigates whether black hole singularities can be resolved within the gauge/gravity duality by focusing on large $N$ gauge theories at strong coupling, where the gauge theory is dual to string theory on backgrounds including black holes in AdS spaces. It argues that finite-temperature ${\cal N}=4$ U($N$) SYM is equivalent to string theory on an asymptotically $AdS_5$ black hole background, with the gauge theory encoding regions behind the horizon and even the singular interior through the $SO(2,4)$ symmetry and the decoupling limit. The key result is that the gauge theory provides a nonsingular, complete description of the spacetime region behind the horizon, suggesting a gauge-theoretic resolution of the classical singularity, and this construction extends to near-extremal M-theory branes and black strings (including BTZ-like cases). The work highlights the potential of holography to reconcile black hole interiors with a well-defined quantum description and motivates further study of the causal structure and infalling observer dynamics from the gauge theory side.

Abstract

We point out that the recent conjecture relating large N gauge theories to string theory in anti-de Sitter spaces offers a resolution in principle of many problems in black hole physics. This is because the gauge theory also describes spacetimes which are not anti-de Sitter, and include black hole horizons and curvature singularities.

Figures (2)

• Figure 1: Causal structure for the near-extreme 3-brane. Each point represents $S^5 \times R^3$.
• Figure 2: Causal structure for the decoupled region.