# Stellar equilibrium in semiclassical gravity

## TL;DR

This paper derives and solves the first exact semiclassical equations for relativistic stars, incorporating quantum vacuum polarization effects, leading to novel solutions that blend black star and gravastar features.

## Contribution

It introduces the first exact solutions of stellar equilibrium equations that include non-perturbative semiclassical backreaction effects.

## Key findings

- Derived semiclassical stellar equilibrium equations in the Polyakov approximation.
- Found exact solutions describing relativistic stars with quantum vacuum effects.
- Identified solutions as a combination of black star and gravastar models.

## Abstract

The phenomenon of quantum vacuum polarization in the presence of a gravitational field is well understood and is expected to have a physical reality, but studies of its back-reaction on the dynamics of spacetime are practically non-existent outside the specific context of homogeneous cosmologies. Building on previous results of quantum field theory in curved spacetimes, in this letter we first derive the semiclassical equations of stellar equilibrium in the s-wave Polyakov approximation. It is highlighted that incorporating the polarization of the quantum vacuum leads to a generalization of the classical Tolman-Oppenheimer-Volkoff equation. Despite the complexity of the resulting field equations, it is possible to find exact solutions. Aside from being the first known exact solutions that describe relativistic stars including the non-perturbative backreaction of semiclassical effects, these are identified as a non-trivial combination of the black star and gravastar proposals.