Black Holes Thermodynamics in a new kind of Noncommutative Geometry

TL;DR

This paper introduces a novel energy-dependent noncommutative geometry inspired by gravity's rainbow, analyzing its effects on black hole thermodynamics and showing that black remnants cannot form due to increased temperature corrections.

Contribution

It proposes a new energy-dependent noncommutative geometry framework and studies its impact on black hole solutions and thermodynamics, revealing unique properties.

Findings

Black remnants cannot form in the new noncommutative black hole solutions.

The corrected temperature of black holes increases due to the deformation.

Explicit expressions for entropy and temperature are derived.

Abstract

Motivated by the energy dependent metric in gravity's rainbow, we will propose a new kind of energy dependent noncommutative geometry. It will be demonstrated that like gravity's rainbow, this new noncommutative geometry is described by an energy dependent metric. We will analyse the effect of this noncommutative deformation on the Schwarzschild black holes and Kerr black holes. We will perform our analysis by relating the commutative and this new energy dependent noncommutative metrics using an energy dependent Moyal star product. We will also analyze the thermodynamics of these new noncommutative black hole solutions. We will explicitly derive expression for the corrected entropy and temperature for these black hole solutions. It will be demonstrated that for these deformed solutions black remnants cannot form. This is because these correction increase rather than reduce the temperature of the black holes.