Finsler Black Holes Induced by Noncommutative Anholonomic Distributions in Einstein Gravity

TL;DR

This paper explores how quantum spacetime noncommutativity can induce Finsler black holes within Einstein gravity, revealing conditions under which such anisotropic black hole solutions can exist, either via geometric deformations or matter effects.

Contribution

It introduces a framework for modeling Finsler black holes induced by noncommutative geometry within Einstein gravity, including explicit conditions for their existence.

Findings

Derived conditions for noncommutative-induced black hole solutions.

Identified two classes of solutions: geometric deformations and matter-induced.

Extended Schwarzschild metrics to locally anisotropic stationary configurations.

Abstract

We study Finsler black holes induced from Einstein gravity as possible effects of quantum spacetime noncommutativity. Such Finsler models are defined by nonholonomic frames not on tangent bundles but on (pseudo) Riemannian manifolds being compatible with standard theories of physics. We focus on noncommutative deformations of Schwarzschild metrics into locally anisotropic stationary ones with spherical/rotoid symmetry. There are derived the conditions when black hole configurations can be extracted from two classes of exact solutions depending on noncommutative parameters. The first class of metrics is defined by nonholonomic deformations of the gravitational vacuum by noncommutative geometry. The second class of such solutions is induced by noncommutative matter fields and/or effective polarizations of cosmological constants.