Quantum Effects of the Massless Spin One-Half Field in Static Spherically Symmetric Black Hole and Wormhole Spacetimes

The full renormalized stress-energy tensor for the massless spin one-half field is numerically computed on and outside the event horizon of an extreme Reissner-Nordstrom black hole and on and outside the throat of three static spherically symmetric Lorentzian wormhole spacetimes. The field and all spacetimes studied are in a zero temperature vacuum state. We treat the field quantum mechanically on a classical background spacetime governed by general relativity. The full stress-energy tensor is found to be finite and regular for all spacetimes. We make comparisons between the numerical calculation and the analytic approximation found by Groves {\it et~al.} for the full stress-energy tensor. We find that the approximation is very poor in most cases, even getting the wrong sign for many components. For the extreme Reissner-Nordstr\"{o}m black hole, divergences predicted by the analytic approximation of are shown to be nonexistent. Lastly, the results for the full stress-energy tensors for wormholes are analyzed in terms of an arbitrary renormalization parameter to see if the ``exotic" energy condition needed to keep such an object from collapsing are met. No wormhole geometry studied is found to be a self-consistent solution when quantum fluctuations of the spin one-half field are considered. This is in contrast to the results found using the analytic approximation for the massless spin-one half field which predicts that one of the wormholes might have a self-consistent solution, since the stress-energy tensor found satisfies the exotic energy condition.

Grantor dc:publisher

Wake Forest University

Year dc:date.issued

2009

Author dc:creator

• Hirsch, William

• wormhole

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10339/14923

OAI identifier oai:identifier

oai:wakespace.lib.wfu.edu:10339/14923