Noncommutative corrections to classical black holes

TL;DR

This paper computes leading noncommutative corrections to classical Schwarzschild black holes sourced by a scalar field, showing they can surpass post-Newtonian corrections but remain experimentally unobservable.

Contribution

It introduces a method to calculate long-distance noncommutative corrections to black hole metrics up to fourth order in the noncommutative parameter.

Findings

Noncommutative corrections can dominate classical post-Newtonian terms for certain parameters.

Corrections are too small to be detected with current experimental capabilities.

The approach treats the energy-momentum tensor in a semiclassical approximation.

Abstract

We calculate leading long-distance noncommutative corrections to the classical Schwarzschild black hole which is sourced by a massive noncommutative scalar field. The energy-momentum tensor is taken up to ${\cal O}(\ell^4)$ in noncommutative parameter, and is treated in semiclassical (tree level) approximation. These noncommutative corrections can dominate classical post-post-Newtonian corrections providing $\ell > 1/M_P$, however, they are still too small to be observable in present-day experiments.