On Modelling the Surfaces of Celestial Bodies in Quantum Gravity

TL;DR

This paper models the surfaces of celestial bodies in quantum gravity, using the Vilkovisky--DeWitt effective action to ensure regular quantum corrections at the surface, improving upon previous pathological descriptions.

Contribution

It introduces a modified density profile to achieve regular quantum corrections at the surface of stellar models in quantum gravity.

Findings

Identifies divergence issues with previous models at the star's surface.

Proposes a differentiability condition for density profiles to ensure regularity.

Demonstrates a modified profile that yields regular quantum corrections.

Abstract

We discuss how to model the surface of celestial bodies (such as stars) in quantum gravity to ensure the regularity of quantum corrections to classical solutions of general relativity at the surface of such bodies. Specifically, we use the Vilkovisky--DeWitt unique effective action to calculate universal quantum corrections to the exterior metric for a class of stellar models. Previous descriptions, obtained via a Heaviside density profile, are ``pathological'' at the surface of the star due to the divergence of the metric functions and associated curvature invariants. Introducing a modified version of the Tolman VII density profile, we determine the minimal degree of differentiability required for this function to generate regular quantum corrections at the star's surface.