The Hawking-Page crossover in noncommutative anti-deSitter space

TL;DR

This paper explores how noncommutative geometry modifies Schwarzschild-AdS black holes, leading to a smearing of singularities and a phase transition resembling a van der Waals fluid, with implications for gauge-string duality.

Contribution

It derives a noncommutative Schwarzschild-AdS solution and analyzes its thermodynamics, revealing a crossover replacing the Hawking-Page transition and identifying a critical point in the phase diagram.

Findings

Curvature singularity is smeared out by noncommutative effects.

Black hole temperature has a maximum, avoiding divergence.

Phase diagram shows a van der Waals-like crossover with a critical point.

Abstract

We study the problem of a Schwarzschild-anti-deSitter black hole in a noncommutative geometry framework, thought to be an effective description of quantum-gravitational spacetime. As a first step we derive the noncommutative geometry inspired Schwarzschild-anti-deSitter solution. After studying the horizon structure, we find that the curvature singularity is smeared out by the noncommutative fluctuations. On the thermodynamics side, we show that the black hole temperature, instead of a divergent behavior at small scales, admits a maximum value. This fact implies an extension of the Hawking-Page transition into a van der Waals-like phase diagram, with a critical point at a critical cosmological constant size in Plank units and a smooth crossover thereafter. We speculate that, in the gauge-string dictionary, this corresponds to the confinement "critical point" in number of colors at finite number of flavors, a highly non-trivial parameter that can be determined through lattice simulations.