Properties of an axisymmetric Lorentzian non-commutative black hole

TL;DR

This paper explores the properties of a rotating non-commutative black hole, analyzing its horizon, thermodynamics, geodesics, shadows, and quasinormal modes to understand its physical characteristics.

Contribution

It introduces a new rotating black hole solution in non-commutative geometry and thoroughly investigates its geometric, thermodynamic, and perturbative properties.

Findings

Modified horizon and ergosphere structures.

Distinct thermodynamic behavior compared to classical black holes.

Characteristic quasinormal mode frequencies for scalar perturbations.

Abstract

In this work, we start by examining a spherically symmetric black hole within the framework of non-commutative geometry and apply a modified Newman-Janis method to obtain a new rotating solution. We then investigate its consequences, focusing on the horizon structure, ergospheres, and the black hole's angular velocity. Following this, a detailed thermodynamic analysis is performed, covering surface gravity, Hawking temperature, entropy, and heat capacity. We also study geodesic motion, with particular emphasis on null geodesics and their associated radial accelerations. Additionally, the photon sphere and the resulting black hole shadows are explored. Finally, we compute the quasinormal modes for scalar perturbations using the 6th-order WKB approximation.