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

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.Comment: 10 pages, RevTex, more typos corrected (combined with arXiv:1003.0614 published in PRD

Casimir effect of two conducting parallel plates in a general weak gravitational field

“…In fact, some non-trivial topologies in curved spacetime do the same job as a boundary does [6,7]. The Casimir energy in curved spacetime has also been analyzed by many authors ( [1,2,6,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and references therein). Recently, a Casimir apparatus consisting of two ideal conducting parallel plates in the weak field limit of the Kerr and the Horava-Lifshitz spacetimes has been studied in [8][9][10][11].…”

Electromagnetic Casimir effect and the spacetime index of refraction

“…So up to now, the boundary conditions on the vector potential are recast into the equations (33) , (34) and (37). Since the scalar field φ inherits the same frequency ω from its parent vector field in (15), from our previous study [5] it is clear that the first condition in (33), φ | ∂M = 0, leads to the frequency shift…”

“…For consistency check purposes, starting from the first equation of (33) and the Klein-Gordon equation for φ, it is an easy task to show that the equation (34) will be obtained. In fact we recall that in [5] it was shown that the Klein-Gordon equation (6) reduces to the following equation for function Z(z)…”

“…In the next section it is shown how one can employ the mode sums used in [5] to obtain the frequency shift on the scalar fields into which the vector field (potential) is decomposed as above. That will consequently lead to the frequency shift on the vector potential itself.…”

Geometric Backreaction of Modified Quantum Vacua and Diffeomorphrisim Covariance

“…But care must be taken that expansion (3) is not unique for all frames [7]. Since the stress-energy tensor for the unbounded vacua is normally ordered, the vacuum expectation value of the stress-energy tensor operator is related to the modified vacuum density T µν = ρ vac g µν Here we follow the usual treatment of vacuum as a perfect fluid with density ρ vac [13]. The semiclassical Einstein field equations (EFE's) are therefore written as :…”