Abstract
In this paper we consider a massive vector field in the background of a space-time obtained by certain Z2 quotient of the BTZ black hole. We analyse the back reaction of the matter field on the space-time geometry up to first order in metric perturbation. The expectation value of the stress-energy tensor can be computed exactly by considering its pull-back onto the covering space. Upon a suitable choice of the boundary condition on the vector field around a non-contractible cycle of the quotient manifold it is possible to obtain the average energy on a null geodesic to be negative there by resulting a traversable wormhole.
Highlights
Wormholes are solutions to Einstein equations which connect two otherwise distinct space-times or two widely separated regions of the same space-time via a throat
Space-times that possess only achronal null geodesics do not admit traversable wormholes. These results have their origin lies in the topological censorship theorem [8] and its generalization to asymptotically locally anti–de Sitter (AdS) spaces [9], which states that every causal curve whose end points lie in the boundary at infinity (I) can be deformed to a causal curve which entirely lies in I itself
Substituting the above for γðμÞ in (3.9), we find that the two-point function for the massive vector field AμðxÞ in AdS3 has the form hAδðxÞAσ0 ðx0Þi 1⁄4 αðμÞgδσ0 ðx; x0Þ þ βðμÞnδðx; x0Þnσ0 ðx; x0Þ ð3:16Þ
Summary
Wormholes are solutions to Einstein equations which connect two otherwise distinct space-times or two widely separated regions of the same space-time via a throat. A traversable wormhole in four dimensions has been devised in [13] by joining the throats of two charged extremal black hole geometries in the presence of massless fermions This construction did not depend on any nonlocal external coupling between the two boundaries and resulted to what are called as the self-supporting wormholes which arise entirely from local dynamics of the fermion fields present in the bulk of the space-time. For AdS3 it is possible to obtain an exact analytic expression for the propagator in closed form Using this result we compute the expectation value of the stress tensor and show that under imposing suitable boundary conditions, this gives rise to traversable wormholes.
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