Quasi-normal modes of quantum gravity black hole with perfectly fluid dark matter

TL;DR

This work analyzes perturbations of a quantum-corrected Schwarzschild black hole surrounded by perfectly fluid dark matter (PFDM) using RG-improvement. It derives the photon sphere and shadow characteristics and computes quasi-normal modes for scalar and electromagnetic fields via a WKB approach, showing that PFDM parameter $\zeta$ and the RG parameter $\tilde{\omega}$ jointly shape the effective potential barriers. The results reveal a turning point near $\zeta\approx0.8$, where the shadow radius $R_s$ is minimized and QNFs reach maximal values, with scalar perturbations generally producing larger frequencies than electromagnetic ones. An eikonal analysis ties the real part of QNFs to the shadow radius through $\omega_R \approx l/R_s$, highlighting a practical link between gravitational-wave signatures and black hole imaging in this quantum-corrected PFDM context.

Abstract

In this work, we have studied the motion of a massless scalar photon in the renormalization group (RG) improved Schwarzschild black hole spacetime in the presence of perfectly fluid dark matter (PFDM). Considering the critical orbit conditions and the null geodesics condition in static spherically sym- In metric geometry, we have shown the variation of the radius of the photon sphere $r_{ph}$ with the PFDM parameter $ζ$. Due to perturbations in black hole spacetime, gravitational waves are emitted in the form of quasi-normal radiations, which correspond to quasi-normal modes (QNMs). In this work, we have studied two types of perturbations in RG improved Schwarzschild spacetime: scalar field perturbations and electromagnetic (EM) field perturbations. For both cases, we have studied the effect of the PFDM parameter on the quasi-normal mode frequencies and the shadow of the black hole, which is related to the photon radius.

Figures (11)

• Figure 1: Construction of black hole shadow perlick.
• Figure 2: Diagram for celestial coordinates $\alpha$ and $\beta$smg.
• Figure 3: Comparison of effective potentials for scalar field perturbations for $l = 1, 2, 3$ at different values of $\zeta$.
• Figure 4: behaviour of Q(x) dasrczettiliqm.
• Figure 5: Comparison of effective potentials for electromagnetic field perturbations for $l = 1, 2, 3$ at different values of $\zeta$.