A Non-Commutative Kalb-Ramond Black Hole

TL;DR

This paper introduces a non-commutative black hole solution in Kalb-Ramond gravity, analyzing its geometry, thermodynamics, quantum radiation, and observational bounds on non-commutative parameters.

Contribution

It presents the first non-commutative Kalb-Ramond black hole solution using Moyal twist and explores its physical and observational properties.

Findings

The black hole lacks spherical symmetry but has an unaffected event horizon.

The solution is regular without second-order non-commutative corrections.

Quantum radiation analysis shows bosons dominate at low frequencies.

Abstract

This work presents a new black hole solution within the framework of a non-commutative gauge theory applied to Kalb-Ramond gravity. Using the method recently proposed in the literature [Nucl.Phys.B 1017 (2025) 116950], we employ the Moyal twist $\partial_r \wedge \partial_\theta$ to implement non-commutativity, being encoded by parameter $\Theta$. We begin by verifying that the resulting black hole no longer possesses spherical symmetry, while the event horizon remains unaffected by non-commutative corrections. The Kretschmann scalar is computed to assess the corresponding regularity. It turns out that the solution is regular, provided that the Christoffel symbols and related quantities are not expanded to second order in $\Theta$. We derive the thermodynamic quantities, including the Hawking temperature $T^{(\Theta,\ell)}$, entropy $S^{(\Theta,\ell)}$, and heat capacity $C_V^{(\Theta,\ell)}$. The remnant mass $M_{\text{rem}}$ is estimated by imposing $T^{(\Theta,\ell)} \to 0$, although the absence of a physical remnant indicates complete evaporation. Quantum radiation for bosons and fermions is analyzed via the tunneling method, where divergent integrals are treated using the residue theorem. Notably, in the low-frequency regime, the particle number density for bosons surpasses that of fermions (at least within the scope of the methods considered here). The effective potential for a massless scalar field is obtained perturbatively, enabling the computation of quasinormal modes and the time-domain profiles. Finally, further bounds on $\Theta$ and $\ell$ (Lorentz-violating paramter) are derived from solar system tests, including the perihelion precession of Mercury, light deflection, and the Shapiro time delay.