The black hole shadow of quantum Oppenheimer-Snyder-de Sitter spacetime

TL;DR

This work analyzes the shadow of a loop-quantum-gravity inspired $qOS$-$dS$ black hole, first in the spherically symmetric case and then in a rotating Kerr-like extension obtained via the Newman–Janis algorithm. By deriving and examining null geodesics, Carter constants, and ZAMO-based imaging, the authors identify a single photon ring between the outer horizon $r_+$ and the cosmological horizon $r_0$, and investigate how quantum corrections parameterized by $p$, $q$, and $ ilde{\alpha}$ modify shadow size, photon ring strength, and image brightness, especially near the cosmological horizon. They employ the GYOTO ray-tracing code to generate simulated images, showing that OSCO adds an outer image edge and that quantum corrections tend to reduce image size while accentuating the photon ring, offering potential observational tests for LQG-inspired modifications. The study provides a framework to constrain quantum gravity effects through black hole imaging in de-Sitter-like spacetimes and highlights several theoretical and methodological limitations for future work.

Abstract

In this study, we investigate the black hole shadow of an exact black hole solution of the loop quantum gravity (LQG) theory. We discuss some of its optical characteristics after generalizing it to the rotational case, including null geodesics and black hole shadow. From these we can compare the impact of different theories on the most deeply understood characteristics of the black hole and get a new way to test the accuracy of the modified gravity theory.

Figures (14)

• Figure 1: The relation between some given parameters and the relative ratio of the three horizon radius.
• Figure 2: $p-q$ diagram and different domains for different behaviors of the effective potential.
• Figure 3: $V(r),V'(r),V"(r)$ as a function of $r$ from $r_{+}$ to $r_{0}$ under parameters $p=0.5,q=0.5$ in A domain.
• Figure 4: $V(r),V'(r),V"(r)$ as a function of $r$ from $r_{+}$ to $r_{0}$ under parameters $p=0.7,q=0.85$ in B domain.
• Figure 5: $V(r),V'(r),V"(r)$ as a function of $r$ from $r_{+}$ to $r_{0}$ under parameters $p=0.7,q=0.92$ in S domain.