Quantum fields in boson star spacetime

TL;DR

This paper investigates the quantum properties of boson star spacetimes by computing quantum scalar fields and stress tensors, revealing significant quantum effects in regions of strong curvature and implications for classical solutions.

Contribution

It introduces a method to compute quantum stress tensors in boson star spacetimes, including regularization and numerical techniques, and compares quantum fluctuations with classical stress.

Findings

Quantum effects are significant in high-curvature regions.

Quantum energy density is mostly positive, but radial pressure is negative.

Quantum fluctuations can be a substantial part of the total stress tensor.

Abstract

Boson stars have been extensively studied in classical gravity, but their quantum properties remain comparatively unexplored. In this paper, we compute the quantum scalar fields and stress tensor in boson star spacetimes within the framework of semiclassical gravity. Divergences are regularized using Pauli-Villars fields, and accurate numerical results are obtained through spectral methods. Employing coherent states enables a direct comparison between the classical part of the stress tensor and the quantum fluctuation. Our results indicate that strong spacetime curvature is the primary source of large quantum effects. The renormalized quantum energy density is mostly positive but the radial pressure is negative, suggesting that classical boson star solutions require modification once quantum effects are included. Moreover, in regimes of large curvature, the quantum fluctuations can constitute a significant fraction of the total stress tensor. The methods developed here can be generalized to other compact objects and used to study their response to quantum corrections.