 
Summary: Stress tensor from the trace anomaly in ReissnerNordstro¨m spacetimes
Paul R. Anderson*
Department of Physics, Wake Forest University, WinstonSalem, North Carolina 27109, USA,
and Racah Institute of Physics, Hebrew University of Jerusalem, Givat Ram, Jerusalem, 91904, Israel
Emil Mottola
Theoretical Division, T8 Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
Ruslan Vaulin
Department of Physics, University of WisconsinMilwaukee, Milwaukee, Wisconsin 53211, USA
(Received 13 August 2007; published 21 December 2007)
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 ReissnerNordstro¨m 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. The approximation scheme
based on the auxiliary field effective action reproduces all physically allowed behaviors of the quantum
stress tensor, in a variety of quantum states, for fields of any spin, in the vicinity of the entire family
