Semiclassical constant-density spheres in a regularized Polyakov approximation

TL;DR

This paper thoroughly analyzes semiclassical effects on constant-density spheres, revealing that quantum corrections enable ultra-compact configurations and challenge classical limits like Buchdahl's, using a regularized Polyakov approximation.

Contribution

It provides a complete catalogue of semiclassical solutions for constant-density spheres, highlighting the importance of quantum effects in high-compactness scenarios.

Findings

Semiclassical corrections enable ultra-compact equilibrium configurations.

No evidence of a Buchdahl limit in semiclassical gravity.

Regularized Polyakov approximation needs improvement for highly compact, regular solutions.

Abstract

We provide an exhaustive analysis of the complete set of solutions of the equations of stellar equilibrium under semiclassical effects. As classical matter we use a perfect fluid of constant density; as the semiclassical source we use the renormalized stress-energy tensor (RSET) of a minimally coupled massless scalar field in the Boulware vacuum (the only vacuum consistent with asymptotic flatness and staticity). For the RSET we use a regularized version of the Polyakov approximation. We present a complete catalogue of the semiclassical self-consistent solutions which incorporates regular as well as singular solutions, showing that the semiclassical corrections are highly relevant in scenarios of high compactness. Semiclassical corrections allow the existence of ultra-compact equilibrium configurations which have bounded pressures and masses up to a central core of Planckian radius, precisely where the regularized Polyakov approximation is not accurate. Our analysis strongly suggests the absence of a Buchdahl limit in semiclasical gravity, while indicating that the regularized Polyakov approximation used here must be improved to describe equilibrium configurations of arbitrary compactness that remain regular at the center of spherical symmetry.