1996/01/29 by David Hochberg, Sergey V. Sushkov, Sergey Sushkov
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Black hole (networking) #Cosmology and Gravitation Theories #Event horizon #General relativity #Mathematical physics #Mathematics #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Schwarzschild metric #Semiclassical physics #Spacetime #Upper and lower bounds #gr-qc
paper · pdf · doi:10.1103/physrevd.53.7094
published as Phys.Rev. D53 (1996) 7094-7102 · 21 pages in plain LaTex. Three figures available upon request from the first author
arxiv created 1996/01/29 · openalex publication_date 1996/06/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
An approximate form for the vacuum averaged stress-energy tensor of a conformal spin-2 quantum field on a black hole background is employed as a source term in the semiclassical Einstein equations. Analytic corrections to the Schwarzschild metric are obtained to first order in \ensuremathε=\ensuremath\Elzxh/M2, where M denotes the mass of the black hole. The approximate tensor possesses the exact trace anomaly and the proper asymptotic behavior at spatial infinity is conserved with respect to the background metric and is uniquely defined up to a free parameter c^2, which relates to the average quantum fluctuation of the field at the horizon. We are able to determine and calculate an explicit upper bound on c^2 by requiring that the entropy due to the back reaction be a positive increasing function in r. A lower bound for c^2 can be established by requiring that the metric perturbations be uniformly small throughout the region 2M\ensuremath≤rr0 where r0 is the radius of perturbative validity of the modified metric. Additional insight into the nature of the perturbed spacetime outside the black hole is provided by studying the effective potential for test particles in the vicinity of the horizon. \textcopyright 1996 The American Physical Society.