Vacuum energy and the spacetime index of refraction: A new synthesis

TL;DR

This paper proposes a novel analogy between spacetime in general relativity and a medium with an index of refraction, linking it to quantum vacuum effects like Casimir energy in curved spacetime.

Contribution

It introduces a new synthesis connecting spacetime's index of refraction with quantum vacuum phenomena, extending the analogy to virtual photon propagation in curved backgrounds.

Findings

Explicit results for Casimir energy near a Kerr black hole

Analysis of vacuum energy response to stationary gravitational fields

Extension of the spacetime-medium analogy to quantum vacuum effects

Abstract

In 1+3 (threading) formulation of general relativity spacetime behaves analogous to a medium with a specific index of refraction with respect to the light propagation. Accepting the reality of zero point energy, through the equivalence principle, we elevate this analogy to the case of virtual photon propagation in a quantum vacuum in a curved background spacetime. Employing this new idea one could examine the response of vacuum energy to the presence of a stationary gravitational field in its different quantum field theoretic manifestations such as Casimir effect and Lamb shift. The results are given explicitly for a Casimir apparatus in the weak field limit of a Kerr hole.