A Non-Commutative Kalb-Ramond Black Hole

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.

70 pages, 2 tables, and 23 figures -- version accepted for publication in JCAP

References in corpus (14)

• The Confrontation between General Relativity and Experiment
• Fermions Tunnelling from Black Holes
• The physical interpretation of the spectrum of black hole quasinormal modes
• Noncommutative Black Hole Thermodynamics
• Charged rotating noncommutative black holes
• Symmetry, Gravity and Noncommutativity
• Hawking temperature from tunnelling formalism
• Corrections to Schwarzschild Solution in Noncommutative Gauge Theory of Gravity
• Towards Noncommutative Quantum Black Holes
• Thermodynamics of an Evaporating Schwarzschild Black Hole in Noncommutative Space
• Geodesics structure and deflection angle of electrically charged black holes in gravity with a background Kalb-Ramond field
• Quantum Gravitational Corrections to Particle Creation by Black Holes
• Properties of an axisymmetric Lorentzian non-commutative black hole
• Einstein-Horndeski gravity and the ultra slowly evaporating black hole