An Effective Model for the Quantum Schwarzschild Black Hole: Weak Deflection Angle, Quasinormal Modes and Bounding of Greybody Factor

TL;DR

This paper investigates quantum effects in Schwarzschild black holes by analyzing the weak deflection angle, deriving bounds for greybody factors, and computing Dirac quasinormal modes, providing new insights into their quantum characteristics.

Contribution

It introduces a comprehensive analysis of quantum Schwarzschild black holes, combining geometric, scattering, and quasinormal mode approaches with novel bounds and calculations.

Findings

Precise deflection angle computed using Gauss-Bonnet theorem.

Derived bounds for greybody factors based on potential scattering.

Calculated Dirac quasinormal modes using WKB approximation.

Abstract

In this paper, we thoroughly explore two crucial aspects of a quantum Schwarzschild black solution within four-dimensional space-time: i) the weak deflection angle, ii) the rigorous greybody factor and, iii) the Dirac quasinormal modes}. Our investigation involves employing the Gauss-Bonnet theorem to precisely compute the deflection angle and establishing its correlation with the Einstein ring. Additionally, we derive the rigorous bounds for greybody factors through the utilization of general bounds for reflection and transmission coefficients in the context of Schrodinger-like one-dimensional potential scattering. We also compute the corresponding Dirac quasinormal modes using the WKB approximation. We reduce the Dirac equation to a Schrodinger-like differential equation and solve it with appropriate boundary conditions to obtain the quasinormal frequencies. To visually underscore the quantum effect, we present figures that illustrate the impact of varying the parameter $r_0$, or more specifically, in terms of the parameter $\alpha$. This comprehensive examination enhances our understanding of the quantum characteristics inherent in the Schwarzschild black solution, shedding light on both the deflection angle and greybody factors in a four-dimensional space-time framework.