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Title: Stress tensor from the trace anomaly in Reissner-Nordstroem spacetimes

Abstract

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-Nordstroem 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 (0{<=}Q{<=}M) of RN horizons.

Authors:
; ;  [1]
  1. Department of Physics, Wake Forest University, Winston-Salem, North Carolina 27109 (United States) and Racah Institute of Physics, Hebrew University of Jerusalem, Givat Ram, Jerusalem, 91904 (Israel)
Publication Date:
OSTI Identifier:
21024053
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 76; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.76.124028; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACTION INTEGRAL; ALGORITHMS; APPROXIMATIONS; BLACK HOLES; COMPARATIVE EVALUATIONS; COORDINATES; COSMOLOGY; DIFFERENTIAL EQUATIONS; EXPECTATION VALUE; FIELD EQUATIONS; MATHEMATICAL SOLUTIONS; SCALARS; SPACE-TIME; SPIN; STRESSES; TENSORS

Citation Formats

Anderson, Paul R, Mottola, Emil, Vaulin, Ruslan, Theoretical Division, T-8 Los Alamos National Laboratory, Los Alamos, New Mexico 87545, and Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53211. Stress tensor from the trace anomaly in Reissner-Nordstroem spacetimes. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.76.124028.
Anderson, Paul R, Mottola, Emil, Vaulin, Ruslan, Theoretical Division, T-8 Los Alamos National Laboratory, Los Alamos, New Mexico 87545, & Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53211. Stress tensor from the trace anomaly in Reissner-Nordstroem spacetimes. United States. https://doi.org/10.1103/PHYSREVD.76.124028
Anderson, Paul R, Mottola, Emil, Vaulin, Ruslan, Theoretical Division, T-8 Los Alamos National Laboratory, Los Alamos, New Mexico 87545, and Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53211. 2007. "Stress tensor from the trace anomaly in Reissner-Nordstroem spacetimes". United States. https://doi.org/10.1103/PHYSREVD.76.124028.
@article{osti_21024053,
title = {Stress tensor from the trace anomaly in Reissner-Nordstroem spacetimes},
author = {Anderson, Paul R and Mottola, Emil and Vaulin, Ruslan and Theoretical Division, T-8 Los Alamos National Laboratory, Los Alamos, New Mexico 87545 and Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53211},
abstractNote = {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-Nordstroem 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 (0{<=}Q{<=}M) of RN horizons.},
doi = {10.1103/PHYSREVD.76.124028},
url = {https://www.osti.gov/biblio/21024053}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 12,
volume = 76,
place = {United States},
year = {Sat Dec 15 00:00:00 EST 2007},
month = {Sat Dec 15 00:00:00 EST 2007}
}