Quantum fields in boson star spacetime

TL;DR

This work investigates quantum scalar fields in boson-star spacetimes within semiclassical gravity by computing the renormalized stress tensor using Pauli-Villars regularization and spectral methods, with coherent states separating the classical and quantum contributions. It finds that strong spacetime curvature is the primary source of large quantum effects, yielding a renormalized energy density that is mostly positive while the radial pressure is negative, signaling backreaction on the classical boson-star solution. Quantum fluctuations can become a substantial fraction of the total stress tensor in highly curved regions, indicating that classical boson-star configurations generally require quantum backreaction to reach true equilibrium. The methods developed are broadly applicable to other compact objects and can be extended to study their response to quantum corrections and potential self-consistent semiclassical configurations.

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.

Figures (12)

• Figure 1: Quantum energy density from summation over different numbers of modes (upper) and extrapolation to the infinite-mode limit using polynomials of different degrees (lower) for the maximum compactness boson star spacetime (left) and Minkowski spacetime (right).
• Figure 2: Quantum energy density (left) and radial pressure (right) at fixed locations, obtained from summation over different numbers of modes, for the maximum compactness boson star spacetime.
• Figure 3: Boson star solutions at maximum mass ($\hat{s}_0=1.24$) and maximum compactness ($\hat{s}_0=1.92$).
• Figure 4: Mass, radius, and compactness of classical boson stars. The upper two panels use the monotonic parameter $\hat{s}_0$ as their horizontal axes, while the lower two panels use the frequency $\omega$.
• Figure 5: Ricci scalar of classical boson stars.