Exact Black Hole Solutions in Noncommutative Gravity

TL;DR

This paper constructs the first exact spherically symmetric black hole solution in a noncommutative gravity theory, revealing holographic features and a fuzzy shell structure outside the horizon, with potential extensions to other black hole types.

Contribution

It provides the first nontrivial exact solution in a noncommutative gravity framework based on star products and twists, demonstrating the method's applicability to various symmetric spacetimes.

Findings

Black hole exhibits holographic behavior

Outside horizon has fuzzy shell-like structure

Inside horizon has noncommutative de Sitter geometry

Abstract

An exact spherically symmetric black hole solution of a recently proposed noncommutative gravity theory based on star products and twists is constructed. This is the first nontrivial exact solution of that theory. The resulting noncommutative black hole quite naturally exhibits holographic behavior; outside the horizon it has a fuzzy shell-like structure, inside the horizon it has a noncommutative de Sitter geometry. The star product and twist contain Killing vectors and act non-trivially on tensors except the metric, which is central in the algebra. The method used can be applied whenever there are enough spacetime symmetries. This includes noncommutative versions of rotating and charged black holes and higher-dimensional and cosmological solutions.