2006/07/28 by Herbert W. Hamber, Ruth M. Williams · 11 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Computer science #Cosmology and Gravitation Theories #Covariance #Exponent #Field (mathematics) #Geometry #Gravitation #Gravitational field #High-Energy Particle Collisions Research #Integer (computer science) #Isotropy #Mathematics #Metric (unit) #Physics #Pure mathematics #Quantum mechanics #Scaling #Statistical physics #Statistics #gr-qc #hep-th
paper · pdf · doi:10.1016/j.physletb.2006.10.049
published in Physics Letters B 643(3-4), 228-234 (Elsevier BV) · 14 pages
arxiv created 2006/07/28 · openalex publication_date 2006/11/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Quantum corrections to the classical field equations, induced by a scale dependent gravitational constant, are analyzed in the case of the static isotropic metric. The requirement of general covariance for the resulting non-local effective field equations puts severe restrictions on the nature of the solutions that can be obtained. In general the existence of vacuum solutions to the effective field equations restricts the value of the gravitational scaling exponent ν−1 to be a positive integer greater than one. We give further arguments suggesting that in fact only for ν−1=3 consistent solutions seem to exist in four dimensions.