Semiclassical relativistic stars

TL;DR

This paper demonstrates that semiclassical gravity allows for the existence of ultracompact stars exceeding the Buchdahl limit, using approximations of quantum stress-energy contributions to achieve regular, stable stellar models.

Contribution

It introduces a method to construct regular ultracompact stars beyond classical limits by incorporating semiclassical effects with a refined RSET approximation.

Findings

Stars near black hole compactness have bounded pressures and curvatures.

A minimal deformation of the Polyakov approximation yields regular ultracompact configurations.

Semiclassical effects enable stable stars beyond classical compactness limits.

Abstract

We present strong evidence that semiclassical gravity can give place to self-consistent ultracompact stars beyond the Buchdahl limit. We integrate the semiclassical equations of (spherically symmetric) stellar equilibrium for a constant-density classical fluid. The semiclassical contribution is modelled by a quantum massless scalar field in the only static vacuum state compatible with asymptotic flatness (Boulware vacuum). The Renormalized Stress-Energy Tensor (RSET) is firstly approximated by the analytic Polyakov approximation. This already reveals a crucial difference with respect to purely classical solutions: stars with compactness close to that of a black hole exhibit bounded pressures and curvatures up to a very small central core compared with the star radius. This suggests that a more refined approximation to the RSET at the core may give rise to strictly regular configurations. Following this suggestion, we prove that a minimal deformation of the Polyakov approximation inside the central core is sufficient to produce regular ultracompact stellar configurations.