2006/04/11 by Emil Mottola, Ruslan Vaulin
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum Electrodynamics and Casimir Effect #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.74.064004
published as Phys.Rev. D74 (2006) 064004 · 54 pages, RevTeX4, 8 figures
arxiv created 2006/04/11 · openalex publication_date 2006/09/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
The low energy effective action of gravity in any even dimension generally acquires nonlocal terms associated with the trace anomaly, generated by the quantum fluctuations of massless fields. The local auxiliary field description of this effective action in four dimensions requires two additional scalar fields, not contained in classical general relativity, which remain relevant at macroscopic distance scales. The auxiliary scalar fields depend upon boundary conditions for their complete specification, and therefore carry global information about the geometry and macroscopic quantum state of the gravitational field. The scalar potentials also provide coordinate invariant order parameters describing the conformal behavior and divergences of the stress tensor on event horizons. We compute the stress tensor due to the anomaly in terms of its auxiliary scalar potentials in a number of concrete examples, including the Rindler wedge, the Schwarzschild geometry, and de Sitter spacetime. In all of these cases, a small number of classical order parameters completely determine the divergent behaviors allowed on the horizon, and yield qualitatively correct global approximations to the renormalized expectation value of the quantum stress tensor.