Method to compute the stress-energy tensor of a spin 1/2 field in a static spherically symmetric spacetime.

摘要

A method for computing the stress-energy tensor for massive or massless quantized spin ½ fields in a general static spherically symmetric spacetime is presented. The fields may be in a zero temperature vacuum state, or a thermal state at an arbitrary temperature. In this method, the renormalized stress-energy tensor is written as the sum of a piece that serves as an analytical approximation, and a numerical piece. Each of these stress-energy tensor pieces is conserved. For the massless case, the trace of the analytical approximation to the stress-energy tensor produces the well-known conformal anomaly, while the numerical piece is traceless. The analytic approximation for the stress-energy tensor for the massless field is equivalent to the approximation of Frolov and Zel'nikov if their expression is evaluated for a static spherically symmetric spacetime, and their arbitrary undetermined coefficients have certain values. The approximation therefore also agrees for the massless case with that of Brown, Ottewill, and Page in Schwarzschild spacetime.