Stress Tensor from the Trace Anomaly in Reissner-Nordstrom Spacetimes

Understand

The effective action associated with the trace anomaly provides a general algorithm for approximating the expectation value of the stress tensor of conformal matter fields in arbitrary curved spacetimes.

• In static, spherically symmetric spacetimes, the algorithm involves solving a fourth order linear differential equation in the radial coordinate r for the two scalar auxiliary fields appearing in the anomaly action, and its corresponding stress tensor.
• By appropriate choice of the homogeneous solutions of the auxiliary field equations, we show that it is possible to obtain finite stress tensors on all Reissner-Nordstrom event horizons, including the extreme Q=M case.
• We compare these finite results to previous analytic approximation methods, which yield invariably an infinite stress-energy on charged black hole horizons, as well as with detailed numerical calculations that indicate the contrary.