Semiclassical Gravity in the Far Field Limit of Stars, Black Holes, and Wormholes

TL;DR

This paper analyzes semiclassical gravity effects in various static, spherically symmetric spacetimes, computing stress-energy tensors for massless fields and revealing their asymptotic behavior and dependence on geometry.

Contribution

It provides a comprehensive analysis of stress-energy tensors for massless fields in diverse spacetimes, combining analytical, numerical, and approximation methods.

Findings

Energy density and pressure scale as 1/r^5 in the far field.

Stress-energy tensor depends only on leading order geometry for certain fields.

Differences in behavior for wormhole spacetimes compared to stars and black holes.

Abstract

Semiclassical gravity is investigated in a large class of asymptotically flat, static, spherically symmetric spacetimes including those containing static stars, black holes, and wormholes. Specifically the stress-energy tensors of massless free spin 0 and spin 1/2 fields are computed to leading order in the asymptotic regions of these spacetimes. This is done for spin 0 fields in Schwarzschild spacetime using a WKB approximation. It is done numerically for the spin 1/2 field in Schwarzschild, extreme Reissner-Nordstrom, and various wormhole spacetimes. And it is done by finding analytic solutions to the leading order mode equations in a large class of asymptotically flat static spherically symmetric spacetimes. Agreement is shown between these various computational methods. It is found that for all of the spacetimes considered, the energy density and pressure in the asymptotic region are proportional to 1/r^5 to leading order. Furthermore, for the spin 1/2 field and the conformally coupled scalar field, the stress-energy tensor depends only on the leading order geometry in the far field limit. This is also true for the minimally coupled scalar field for spacetimes containing either a static star or a black hole, but not for spacetimes containing a wormhole.