Noncommutative black hole in de Rham-Gabadadze-Tolley like massive gravity

TL;DR

This paper explores the properties of noncommutative Schwarzschild black holes within a massive gravity framework, analyzing horizons, thermodynamics, perturbations, quasinormal modes, and shadow characteristics, revealing effects of noncommutativity and graviton mass.

Contribution

It introduces a comprehensive study of noncommutative black holes in massive gravity, including thermodynamics, stability, quasinormal modes, and shadow analysis, highlighting the influence of noncommutativity and graviton mass.

Findings

Existence of stable black hole remnants with mass depending on noncommutative parameter and graviton mass.

All quasinormal modes have negative imaginary parts, indicating stability.

Noncommutativity reduces black hole shadow size, while graviton mass increases it at larger distances.

Abstract

We examine the behavior of non-commutative Schwarzschild black holes in the context of massive gravity. According to the investigation, corresponding to a minimal mass, the black hole can have two horizons, one horizon, or no horizon at all. Our results imply the existence of a stable black hole remnant, whose mass can be uniquely calculated in terms of the non-commutative parameter $\theta$ and gravity mass $m$. Thermodynamic features such as heat capacity and Hawking temperature are studied. We also examine a scalar linear perturbation on the black hole. Quasinormal frequencies are computed via Wentzel-Kramers-Brillouin(WKB) method with Pade improvement. All quasinormal frequencies considered in this work have a negative imaginary part. In the eikonal limit, we investigate the angular velocity and the Lyapunov exponent as a function of $M/\sqrt{\theta}$. Additionally, we explore the black hole's shadow across various model parameters. Our findings indicate that non-commutativity leads to a reduction in the black hole's shadow, with this effect exhibiting a nonlinear relationship. Furthermore, we observe that the inclusion of a massive graviton in the theory results in an increase in the black hole's shadow radius, particularly at greater observer distances.