Conformal invariance and apparent universality of semiclassical gravity

TL;DR

This paper demonstrates that in higher-dimensional static spherically symmetric spacetimes, certain quantum field observables exhibit universal behavior at large distances, independent of the internal structure of the gravitational source, especially for conformally invariant scalar fields.

Contribution

It generalizes the universality of quantum observables in semiclassical gravity to higher dimensions and computes explicit expressions for <T^{}>, including quantum corrections to gravitational potentials.

Findings

Universality of <T^{}> in Db4b4 b4b4 dimensions.

Explicit quantum corrections to gravitational potential in D dimensions.

Agreement with known one-loop graviton propagator corrections in D=4.

Abstract

In a recent work, it has been pointed out that certain observables of the massless scalar field theory in a static spherically symmetric background exhibit a universal behavior at large distances. More precisely, it was shown that, unlike what happens in the case the coupling to the curvature \xi is generic, for the special cases \xi=0 and \xi = 1/6 the large distance behavior of the expectation value <T^{\mu}_{\nu}> turns out to be independent of the internal structure of the gravitational source. Here, we address a higher dimensional generalization of this result: We first compute the difference between a black hole and a static spherically symmetric star for the observables <\phi^2> and <T^{\mu}_{\nu}> in the far field limit. Thus, we show that the conformally invariant massless scalar field theory in a static spherically symmetric background exhibits such universality phenomenon in D\geq 4 dimensions. Also, using the one-loop effective action, we compute <T^{\mu}_{\nu}> for a weakly gravitating object. These results lead to the explicit expression of the expectation value <T^{\mu}_{\nu}> for a Schwarzschild-Tangherlini black hole in the far field limit. As an application, we obtain quantum corrections to the gravitational potential in D dimensions, which for D=4 are shown to agree with the one-loop correction to the graviton propagator previously found in the literature.