Smeared BTZ Black Hole from Space Noncommutativity

TL;DR

This paper explores how space noncommutativity causes black hole horizons to smear, leading to novel properties such as finite signal escape times and altered thermodynamics in a smeared BTZ black hole within $AdS_3$ space.

Contribution

It provides an explicit example of horizon smearing due to space noncommutativity in $AdS_3$ using Chern-Simons gravity, revealing new horizon structures and thermodynamic behaviors.

Findings

Horizon splitting and smearing occur due to noncommutativity.

Signals can escape the smeared black hole in finite time.

Hawking temperature is ill-defined except in non-rotating cases.

Abstract

We study a novel phenomena of smearing of black hole horizons from the effect of space noncommutativity. We present an explicit example in $AdS_3$ space, using the Chern-Simons formulation of gravity. This produces a smeared BTZ black hole which goes beyond the classical spacetime unexpectedly and there is {\it no} reality problem in our approach with the gauge group $U(1,1) \times U(1,1)$. The horizons are smeared, due to a splitting of the Killing horizon and the apparent horizon, and there is a metric signature change to Euclidean in the smeared region. The inner boundary of the smeared region acts as a trapped surface for timelike particles but the outer as a classical barrier for ingoing particles. The lightlike signals can escape from or reach the smeared region in a {\it finite} time, which indicates that {\it the black hole is not so dark, even classically.} In addition, it is remarked that the Hawking temperature can {\it not} be defined by the regularity in the Euclidean geometry except in the non-rotating case, and the origin can be smeared by a {\it new} (apparent) horizon.