Abstract
We have investigated the Unruh effect in Anti de-Sitter (AdS) spacetime by examining the response function of an Unruh-DeWitt particle detector with uniform constant acceleration. An exact expression of the detector response function for the scalar field has been obtained with different levels of non-linearity in even dimensional AdS spacetime. We also showed how the response of the accelerated Unruh detector coupled quadratically to massless Dirac field in D dimensional (D ≥ 2) AdS spacetime is proportional to that of a detector linearly coupled to a massless scalar field in 2D dimensional AdS spacetime. Here, the fermionic and scalar matter field is coupled minimally and conformally to the background AdS metric, respectively. Finally, we discuss about the extension of the results for more general stationary motion.
Highlights
We have investigated the Unruh effect in Anti de-Sitter (AdS) spacetime by examining the response function of an Unruh-DeWitt particle detector with uniform constant acceleration
We showed how the response of the accelerated Unruh detector coupled quadratically to massless Dirac field in D dimensional (D ≥ 2) AdS spacetime is proportional to that of a detector linearly coupled to a massless scalar field in 2D dimensional AdS spacetime
Explicit computations are available for the detector response function in D dimensional Minkowski spacetime where a peculiar trend of “inversion of statistics” has been noticed in odd dimensions for linearly coupled detectors with a scalar field [52,53,54]
Summary
We first study a real scalar field Φ in D dimensional AdS spacetime which is conformally coupled to gravitational background. One can construct a path with constant acceleration by considering it as a intersection between a M (M < D + 1) dimensional flat plane and D dimensional AdS hypersurface embedded in D + 1 dimensional flat spacetime. In appendix C we have employed global embedding approach to show that for all uniform linear supercritical trajectories confined between the intersection of a two dimensional plane and AdS hypersurface would have the same conformal invariant v as a function of proper time. If one takes the Fourier transform of the correlation function it becomes proportional to the Bose/Fermi distribution depending upon the periodic or anti-periodic condition respectively, G. Theorem 1 The detector response function of massless scalar fields coupled to the detector according to eq (1.7) for any uniform linear accelerated path for (D > 2) dimensional AdS spacetime defined is equal to.
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