2006/02/28 by Wolfgang Graf
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Astrophysics #Classical field theory #Classical mechanics #Cosmology #Cosmology and Gravitation Theories #Einstein #Geometric Analysis and Curvature Flows #Geometry #Gravitation #Higher-dimensional Einstein gravity #Introduction to the mathematics of general relativity #Mathematical physics #Mathematics #Parameterized post-Newtonian formalism #Physics #Quantum gravity #Quantum mechanics #Ricci flow #Scalar (mathematics) #Scalar curvature #Semiclassical gravity #Theoretical physics #astro-ph #f(R) gravity #gr-qc #hep-th #math.DG
paper · pdf · doi:10.1186/1754-0410-1-3
published as PMCPhys.A1:3,2007 · 15 pages. V2: improved presentation, in particular Jordan vs. Brans-Dicke and on viability. Added section on physical interpretation. V3: more references. Reworked to agree with published version
openalex publication_date 2007/10/02 · arxiv created 2007/10/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A theory of gravitation is proposed, modeled after the notion of a Ricci flow . In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gravity. In particular there is no adjustable coupling constant. For the solar system the effects of Ricci flow gravity cannot be distinguished from Einstein gravity and therefore it passes all classical tests. However for cosmology significant deviations from standard Einstein cosmology will appear. PACS Codes: 04.50.+h, 04.20.Cv, 02.40.Hw