Conformal invariance and apparent universality of semiclassical gravity

Garbarz, A.; Giribet, G.; Mazzitelli, F. D.

Conformal invariance and apparent universality of semiclassical gravity

Authors

Garbarz, A.

Giribet, G.

Mazzitelli, F. D.

Description

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 ξis generic, for the special cases ξ=0 and ξ= 1/6 the large distance behavior of the expectation value <T^μ_ν> 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 <ϕ^2> and <T^μ_ν> 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^μ_ν> for a weakly gravitating object. These results lead to the explicit expression of the expectation value <T^μ_ν> 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.
11 pages