Strong gravitational lensing in a noncommutative black-hole spacetime

TL;DR

This paper investigates how noncommutative geometry affects strong gravitational lensing around black holes, providing potential observational methods to distinguish noncommutative black holes from charged black holes.

Contribution

It analyzes the impact of spacetime noncommutativity on gravitational lensing in a noncommutative Schwarzschild black hole and compares it to Reissner-Nordström black holes.

Findings

Noncommutative parameter influences lensing similarly to charge but with smaller effects.

Provides estimates for lensing observables in noncommutative black hole spacetime.

Suggests potential to measure noncommutative constant using astronomical observations.

Abstract

Noncommutative geometry may be a starting point to a quantum gravity. We study the influence of the spacetime noncommutative parameter on the strong field gravitational lensing in the noncommutative Schwarzschild black-hole spacetime and obtain the angular position and magnification of the relativistic images. Supposing that the gravitational field of the supermassive central object of the galaxy described by this metric, we estimate the numerical values of the coefficients and observables for strong gravitational lensing. Comparing to the Reissner-Norstr\"{om} black hole, we find that the influences of the spacetime noncommutative parameter is similar to those of the charge, just these influences are much smaller. This may offer a way to distinguish a noncommutative black hole from a Reissner-Norstr\"{om} black hole, and may probe the spacetime noncommutative constant $\vartheta$ \cite{foot} by the astronomical instruments in the future.