Radiation properties and images of loop quantum Reissner-Nordström black hole with a thin accretion disk

TL;DR

The paper tackles how loop-quantum gravity modifications to a Reissner–Nordström black hole (captured by the parameter $\zeta$) affect shadow properties and thin-disk radiation. It derives the LQRNBH metric, computes the photon sphere and shadow radius $R_{sh}$, and analyzes timelike circular orbits including the ISCO radius $R_I$, complemented by a Page-thin-disk radiation model and backward ray-tracing to generate isoradial curves and images. Key findings show that increasing $\zeta$ pushes $R_I$ outward while increasing $Q$ pulls it inward; the shadow depends on $\zeta$ despite unchanged horizons, and the radiation efficiency $\epsilon$ decreases with $\zeta$ but increases with $Q$, with direct and secondary images shrinking under stronger quantum effects. The results yield observational signatures—through shadows and disk images—that could distinguish LQRNBH from classical RN or Schwarzschild black holes, and they provide constraints on $\zeta$ and $Q$ from M87* (and Sgr A*) data to guide future tests of loop quantum gravity in strong gravity regimes.

Abstract

We investigate the characteristics of circular geodesics around loop quantum Reissner-Nordström black hole (LQRNBH) and the radiation properties and observational appearance of a thin accretion disk around it. By calculating the shadow radius and utilizing observational data from M87* and Sgr A*, we derive constraints on the quantum parameter $ζ$ and charge parameter $Q$. The timelike circular geodesics around LQRNBH and the influence of the model parameters on the circular motion are also discussed. It is found that contrary to the case of the parameter $Q$, the increase of the quantum parameter $ζ$ leads to the increase of the radius of the innermost stable circular orbit (ISCO). Then, by considering a thin accretion disk model, various radiation properties of the LQRNBH and the effects of the model parameters on them are studied. Concrete examples are provided for quantitative comparison of the radiation properties between LQRNBH and Schwarzschild black hole. With the ray-tracing method, the isoradial curves, redshift distributions, and the observed radiation fluxes of the direct and secondary images of the LQRNBH with the thin accretion disk for various model parameters and observation angles are numerically calculated and discussed. These results are beneficial for us to understand the physical consequences of loop quantum gravity effect.

Figures (12)

• Figure 1: Constraints on $\zeta$ and $Q$ from the observations of M87* and Sgr A*.
• Figure 2: Energy $E$, angular momentum $L$, and angular velocity $\Omega$ of particles on circular orbits around a LQRNBH with various $\zeta$ (top row) and $Q$ (bottom row).
• Figure 3: (a) Effective potential for particles on circular orbits as a function of the orbital radius. (b) Effective potential for a particle moving off the ISCO after small perturbation. Curves are plotted for various quantum parameter $\zeta$.
• Figure 4: The ISCO radius $R_I$ as a function of parameters $\zeta$ and $Q$.
• Figure 5: The radiation flux $F$ of the thin accretion disk around the LQRNBH for various parameters $\zeta$ and $Q$.