Quantum features of a non-commutative Schwarzschild black hole

TL;DR

This work analyzes quantum features of a Schwarzschild-like black hole in non-commutative gauge gravity constructed with the Moyal twist $\partial_t \wedge \partial_\theta$, showing that the horizon and surface gravity remain at $r_h=2M$ and $\kappa|_{r_h}=1/(4M)$, respectively. Using a semiclassical tunneling framework for bosons and a curved-space Dirac approach for fermions, it derives $\Theta$-dependent corrections to the emission spectra while keeping the Hawking temperature unchanged; fermionic flux is suppressed with larger $\Theta$, and bosonic emission includes backreaction effects. Evaporation is treated via a Stefan–Boltzmann description with a corrected cross section, predicting a higher radiative rate and shorter lifetime as $\Theta$ grows, and the model yields no stable remnant. Finally, solar-system tests (Mercury precession, light deflection, Shapiro delay) place upper bounds on $\Theta^{2}$, validating the perturbative treatment and constraining the scale of non-commutativity in a near-Earth weak-field regime.

Abstract

This work aims to present the quantum aspects of a non-commutative gauge gravity formulation of a Schwarzschild-like black hole constructed via the Moyal twist $\partial_t \wedge \partial_θ$. Particle creation is estimated for bosonic and fermionic fields using the quantum tunneling method, with divergent integrals treated through the residue prescription. Since the surface gravity is well defined for this configuration, the corresponding emission rates and evaporation lifetimes are also computed. In addition, previously reported results in the literature on gauge gravity Schwarzschild black holes are revisited. Finally, we infer constraints on the non-commutative parameter $Θ$ from solar-system tests.

Figures (4)

• Figure 1: Bosonic particle production, quantified by $n(\omega,\Theta)$, is plotted as a function of the energy $\omega$ for different choices of the non--commutative parameter.
• Figure 2: Fermionic particle production spectra $n_{\psi}(\omega,\Theta)$ plotted versus the frequency $\omega$ for different choices of the non--commutative parameter $\Theta$.
• Figure 3: Total evaporation time $t_{\text{evap}}$ as a function of the initial mass $M_i$ for several values of the non--commutative parameter $\Theta$.
• Figure 4: Emission rate as a function of the frequency $\omega$ for different values of the non--commutative parameter $\Theta$.