Strong gravitational lensing effects of black holes with quantum hair

TL;DR

This paper derives a quantum-corrected black hole metric to study how quantum hair influences strong gravitational lensing, revealing that quantum effects alter lensing observables like deflection angles and magnifications.

Contribution

It introduces a novel quantum-corrected black hole metric using the Barvinsky-Vilkovisky formalism without previous assumptions, and analyzes its impact on gravitational lensing effects.

Findings

Quantum hair increases the photon sphere radius.

Quantum hair enhances the strong deflection angle.

Quantum hair decreases the angular separation.

Abstract

According to the no-hair theorem, stationary black holes are uniquely characterized by their mass, charge, and angular momentum. In this paper, we explore quantum hair by deriving the quantum-corrected black hole metric within the Barvinsky-Vilkovisky formalism. The quantum-corrected metric is obtained perturbatively around flat spacetime without assuming either the commutativity between the nonlocal operator and covariant derivatives or the nonlocal Gauss-Bonnet theorem, both of which are adopted in previous studies. Using this metric, we evaluate the deflection angle in the strong-field limit and compute the associated strong gravitational lensing observables, such as the angular separation and the relative magnification. Our results show that as the quantum hair, determined by the number of virtual massless quantum fields in the nonlocal effective action, increases, the photon sphere radius, the strong deflection angle, and the relative magnification all increase, whereas the angular separation decreases. As a result, we demonstrate that the quantum hair affects not only the black hole geometry but also its strong gravitational lensing effects.