Nonlocal stress-energy tensor in time-dependent gravitational backgrounds

TL;DR

This paper investigates the behavior of the renormalized stress-energy tensor of a quantum scalar field in dynamic gravitational backgrounds, revealing local nonvanishing effects at null infinity and quantum corrections to the metric.

Contribution

It provides a formal evaluation of the RSET in arbitrary dimensions, derives its multipole expansion in spherically symmetric spacetimes, and links the total radiated energy to the first-order RSET.

Findings

RSET is nonzero at null infinity and depends on collapse dynamics.

Total emitted energy vanishes at leading order, but can be derived from first-order RSET.

Quantum corrections to the metric are computed at large distances.

Abstract

We analyze the renormalized stress-energy tensor (RSET) of a massless quantum scalar field in time-dependent gravitational backgrounds. Starting from its formal expression obtained within the covariant perturbative expansion to lowest order in the curvature, we evaluate the RSET in an arbitrary number of dimensions in terms of coordinate-space distributions. For time-dependent spherically symmetric spacetimes, we derive a multipole expansion and determine its asymptotic behavior. We find that the RSET is locally nonvanishing at null infinity and depends on the detailed dynamics of the collapsing body. However, the total emitted energy vanishes at this order, meaning that the leading contribution does not account for the energy density of the created particles. Nevertheless, by enforcing stress-tensor conservation up to second order in the curvature, we show that the total radiated energy can be extracted from the first-order RSET. Finally, we compute the induced quantum corrections to the metric at large distances, which display several interesting features.