Quantum Effects on the Deflection of Light and the Gauss-Bonnet Theorem

TL;DR

This paper uses the Gauss-Bonnet theorem to analyze how quantum corrections to Schwarzschild black holes affect light deflection, demonstrating that quantum effects modify the classical deflection angle.

Contribution

It applies the Gauss-Bonnet theorem to quantum-corrected black holes, providing a novel analytical approach to quantify quantum effects on light deflection.

Findings

Quantum corrections alter the light deflection angle.

The Gauss-Bonnet method yields exact leading-order results.

Quantum effects are significant in the weak limit approximation.

Abstract

In this letter we apply the Gauss--Bonnet theorem (GB) to calculate the deflection angle by a quantum corrected Schwarzschild black hole in the weak limit approximation. In particular we calculate the light deflection by two types of quantum corrected black holes: the renormalization group improved Schwarzschild solution and the quantum corrected Schwarzschild solution in Bohmian quantum mechanics. We start from the corresponding optical metrics to use then the GB theorem and calculate the Gaussian curvature in both cases. We calculate the leading terms of the deflection angle and show that quantum corrections modifies the deflection angle in both solutions. Finally by performing geodesics calculations we show that GB method gives exact results in leading order terms.