Probing spacetime noncommutative constant via charged astrophysical black hole lensing

TL;DR

This paper investigates how the noncommutative parameter affects strong gravitational lensing around charged black holes, proposing a potential astronomical method to measure spacetime noncommutativity.

Contribution

It introduces a detailed analysis of lensing observables in noncommutative Reissner-Nordström black holes and identifies the parameter range detectable by future astronomical observations.

Findings

Observables decrease with increasing noncommutative parameter.

Detectable range of the noncommutative parameter is wider than in Schwarzschild case.

Potential to probe spacetime noncommutativity via astrophysical lensing measurements.

Abstract

We study the influence of the spacetime noncommutative parameter on the strong field gravitational lensing in the noncommutative Reissner-Nordstr\"{o}m black-hole spacetime. Supposing that the gravitational field of the supermassive central object of the Galaxy is described by this metric, we estimate the numerical values of the coefficients and observables for strong gravitational lensing. Our results show that with the increase of the parameter $\sqrt{\vartheta}$, the observables $\theta_{\infty}$ and $r_m$ decrease, while $s$ increases. Our results also show that i) if $\sqrt{\vartheta}$ is strong, the observables are close to those of the noncommutative Schwarzschild black hole lensing; ii) if $\sqrt{\vartheta}$ is weak, the observables are close to those of the commutative Reissner-Nordstr\"{o}m black hole lensing; iii) the detectable scope of $\vartheta$ in a noncommutative Reissner-Nordstr\"{o}m black hole lensing is $0.12\leq\sqrt{\vartheta}\leq0.26$, which is wider than that in a noncommutative Schwarzschild black hole lensing, $0.18\leq\sqrt{\vartheta}\leq0.26$. This may offer a way to probe the spacetime noncommutative constant $\vartheta$ by the astronomical instruments in the future.