Smeared BTZ Black Hole from Space Noncommutativity

Abstract

We study a novel phenomena of smearing of black hole horizons from the effect of space noncommutativity. We present an explicit example in $Ad{S}_3$ 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.

Added notes about boundary conditions, NC curvature, and torsion; Accepted in JHEP