Quantum Effects in a Rotating Spacetime

Abstract

The behavior of a arbitrary coupled quantum scalar field is studied in the background of the Gödel spacetime. Closed forms are derived for the effective action and the vacuum expectation value of quadratic field fluctuations by using ζ-function regularization. Based on these results, we argue that causality violation presented in this spacetime can not be removed by quantum effects. Introduction and motivationWhether or not the laws of physics permit the existence of closed timelike curves (CTCs) is one the important problems in the research field of modern theoretical physics. A number of familiar spacetimes make it clear that general relativity, as it is normally formulated, does not exclude the violation of causality in large scale, despite its local Lorentzian character. 1 where Ω and m are constants; m 2 can be continued to negative values, for m 2 → 0 obtaining SomRaychaudhuri spacetime [3]. The solution originally proposed by Gödel corresponds to the case m 2 = 2Ωwhere Ω ≥ 0 is a constant parameter related to the vorticity of the matter, and −∞ < t, z < ∞, 0 ≤ r < ∞, 0 < ϕ ≤ 2π. The source of this geometry is a perfect fluid with constant density ρ and no pressure (p = 0). Einstein's equation's with a cosmological constant Λ are satisfied if between Ω, Λ and ρ the following relation holdsThe study of geodesics showed that this spacetime is geodesically complete (and so singularity free) [4,5].Furthermore, because the universe is spacetime homogeneous, there are CTCs through every event [6] (hence the causal violation is not localized to some small region).In the last decade many authors have studied features of quantum field theory on a spacetime background that contains CTCs but most of the papers are dealing with confined causality violating spacetime.In these, CTCs are confined within some regions and there exist at least one region free of them; the regions with CTCs are separated from the well behaved spacetime by Cauchy horizons. Being a highly symmetric homogeneous spacetime, Gödel spacetime is an excellent model to investigate questions of principle related to the quantization of fields propagating on curved background, the interaction with a global vorticity and the issues related to the lack of global hyperbolicity. Even if one's primary interest is in quantum field theory in a confined causality violating spacetime, we hope that, by widening the context to Gödel spacetime, one may achieve a deeper appreciation of the theory. In particular, one may hopes to attain more general features of a quantum field propagating in a nonglobally hyperbolic spacetime, whether or not containing a Cauchy horizon. Of particular interest is the question whether causality violation which occurs in Gödel spacetime implies divergence of vacuum polarization fluctuations and may be removed by quantum effects. Thus it seems important to study the vacuum polarization for different physical fields in this background. 2A different reason to study quantum field theory (QFT) in this background emerges from the fact ...

New multiply nutty spacetimes

“…Moreover, they have been used to uncover deep results regarding gravitational entropy [2,3,11,12] and, in particular, they exhibit breakdowns of the usual relation between entropy and area [13] (even in the absence of Misner string singularities). Furthermore, it has been recently noted that the boundary metric Lorentzian sector of these spaces in AdS-backgrounds is in fact similar with the Gödel metric [14,15].…”

Nut Charged Space-times and Closed Timelike Curves on the Boundary

“…As noted in ref. [9] (see, also, ref. [10]), the boundary metrics of a four dimensional Lorentzian Taub-NUT-AdS spacetime correspond to the essential threedimensional part of a homogeneous Gödel-type spacetime, and contain closed timelike curves (CTCs) for a large class of parameters [11].…”

Gravitating non-Abelian solutions with a NUT charge

“…Thus asymptotically Taub-NUT-AdS solutions provide an opportunity for the study of quantum field theories on Gödel-type rotating spacetimes, which is clearly an interesting subject [53]. Given all the problems with the Lorentzian interpretation of a Taub-NUT-AdS solution, we should not be surprised if the boundary metric and the living CFT present unphysical properties.…”