Axisymmetric black hole in a non-commutative gauge theory: classical and quantum gravity effects

TL;DR

The paper develops a rotating black hole solution in a non-commutative gauge theory using a modified Newman–Janis construction from a NC Schwarzschild seed with mass $M_\Theta = M - \frac{\Theta^2}{64 M}$. It analyzes horizons, ergospheres, angular velocity, and the full thermodynamic structure, including the Hawking temperature $T(\Theta,a,M)$, entropy $S(\Theta,a,M)$, heat capacity $C_V(\Theta,a,M)$, and remnant mass $M_+(a,\Theta)$, highlighting NC corrections relative to Kerr. Quantum effects are explored via Hawking radiation as tunneling for bosonic and fermionic modes, yielding explicit particle densities $n_b(\omega,\Theta,a,M)$ and $n_f(\omega,\Theta,a,M)$ that generally increase with NC parameter $\Theta$ and spin $a$. The study of geodesics reveals modified null trajectories, a photon sphere, and black hole shadows described by celestial coordinates, with EHT constraints for M87$^*$ translating into bounds on $(a,\Theta)$; strong deflection lensing is analyzed in the SDL, producing NC- and spin-dependent deflection coefficients. Overall, the work demonstrates how non-commutative gauge-theory corrections systematically influence classical black-hole structure, thermodynamics, radiation, and strong-field observables, offering avenues for quantum-gravity phenomenology and future tests with high-precision black-hole imaging and lensing.

Abstract

This work explores both classical and quantum aspects of an axisymmetric black hole within a non-commutative gauge theory. The rotating solution is derived using a modified Newman-Janis procedure. The analysis begins with the horizon structure, ergospheres, and angular velocity. The thermodynamic properties are examined through surface gravity, focusing on the Hawking temperature, entropy, and heat capacity. In addition, the remnant mass is calculated. The Hawking radiation is treated as a tunneling process for bosonic and fermionic particles, along with the corresponding particle creation density. Geodesic motion is explored, emphasizing null geodesics, radial accelerations, the photon sphere, and black hole shadows. Finally, the gravitational lensing in the strong deflection limit is investigated.

Figures (19)

• Figure 1: The parameter $\Delta(r)$ is shown as a function of $r$ for different combinations of $\Theta$ and $a$.
• Figure 2: The top left panel displays the behavior of $r_{+}$ as a function of the mass parameter $M$ for various values of $\Theta$ while keeping the spin parameter fixed at $a = 0.5$. The top right panel illustrates the dependence of $r_{+}$ on $M$ for different spin parameter values, with $\Theta$ held constant at $0.1$. The bottom panel presents a three--dimensional plot of $r_{+}$ as a function of both $a$ and $\Theta$, keeping the mass parameter fixed at $M = 1$.
• Figure 3: The parametric plot of the ergosphere is shown for different combinations of the non--commutative parameter $\Theta$ and the spin parameter $a$.
• Figure 4: The angular velocity $\omega$ is shown in two--dimensional plots for different values of the spin parameter $a$ and the non--commutative parameter $\Theta$.
• Figure 5: The angular velocity $\omega$ is depicted using three--dimensional plots for various values of the spin parameter $a$ and the non--commutative parameter $\Theta$.