Einstein ring of dust shells with quantum hair

Abstract

The information about the internal structure of a compact object is classically inaccessible to external observers. In this paper, we investigate how quantum corrections to gravitational fields can reveal the internal structure of compact objects composed of dust shells. Using an effective field theory approach to incorporate quantum corrections up to second order in curvature, we derive a quantum-corrected metric for $N$ uniformly spaced shells with equal surface mass density and then examine how these corrections manifest in the deflection angle for gravitational lensing. In particular, we mainly investigate quantum-corrected astrophysical observables such as the Einstein ring and image magnification. Compared to the classical scenario, the deflection angle and the corresponding Einstein angle differ by a term that depends explicitly on the number of dust shells, which play the role of quantum hair. Specifically, the quantum correction to them diminishes as $N$ increases, yet a finite deviation from the classical result remains even in the continuum limit $N\to\infty$. Consequently, our results show that the internal structures of compact objects with identical mass and radius can be distinguished by quantum hair through their lensing observables.