Circular orbits and accretion disk around a deformed-Schwarzschild black hole in loop quantum gravity

TL;DR

This work analyzes a loop quantum gravity–inspired deformed Schwarzschild black hole to study neutral and electrically charged particle motion, ISCOs, and accretion-disk radiation within the Novikov–Thorne framework. The quantum-corrected metric introduces a correction parameter $\\alpha$ (with $\\alpha\propto\\gamma^{3}$) that alters horizon structure and geodesics, causing ISCO radii to shrink as $\\gamma$ grows. A Wald-like electromagnetic potential incorporating LQG corrections is constructed to examine charged-particle dynamics, showing consistent ISCO shifts with increasing $\\gamma$. Disk observables—radiative efficiency, flux, temperature, differential luminosity, and spectral luminosity—increase with $\\gamma$, with ISCO-near effects potentially at the threshold of detectability by current or future VLBI, providing a potential indirect probe of quantum gravity effects.

Abstract

In this paper, we study the motion of neutral and electrically charged particles in the vicinity of a deformed-Schwarzschild black hole inspired by Loop Quantum Gravity (LQG). To examine the motion of an electrically charged test particle, we propose an expression for electromagnetic 4-potential that contains the impacts of loop quantum gravity. This electromagnetic 4-potential satisfies approximately the covariant Maxwell's equations to first order in the loop quantum effects. We explore the effects of the loop quantum correction parameter on the particle geodesics. We investigate the innermost stable circular orbits (ISCOs) for both neutral and electrically charged particles in detail, demonstrating that the loop quantum parameter significantly influences on the ISCO radius, causing it to shrink. Finally, we explore the accretion disk around the loop quantum black hole. We delve into the electromagnetic radiation flux, temperature, differential luminosity, and the spectral luminosity as radiation properties of the accretion disk in detail. We show that the loop quantum correction parameter shifts the profile of the electromagnetic flux and accretion disk temperature towards the central object, leading to a slight increase in these quantities.

Figures (10)

• Figure 1: $V_{eff}$ of the static spherically symmetric loop quantum black hole shown against $r$ for a range of $\gamma$ values. The Schwarzschild ($\gamma=0$) and RN solutions are shown by the green and black solid lines, respectively. The colored dots show the locations of ISCOs.
• Figure 2: The plot of $E^{2}$ of the static spherically symmetric loop quantum black hole versus $r$ for different values of $\gamma$. The green and black solid lines are for the case of Schwarzschild and RN solutions, respectively.
• Figure 3: The behavior of $L^{2}$ of the static spherically symmetric loop quantum black hole versus $r$ for various $\gamma$ values. The green and black solid lines represent the Schwarzschild and RN solution, respectively.
• Figure 4: The plot of $\Omega_{\varphi}^{2}$ of the static spherically symmetric loop quantum black hole versus $r$ for various $\gamma$ values. The green and black solid lines represent the Schwarzschild and RN solutions, respectively.
• Figure 5: The effective potential $\tilde{V}_{eff}$ felt by the massive electrically charged test particle moving in the static spherically symmetric loop quantum black hole's spacetime as a function of $r$ for various $\gamma$ values. The Schwarzschild solution situation in GR is shown by the green solid line.