2007/05/09 by Joseph Samuel, Sutirtha Roy Chowdhury · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Geometric Analysis and Curvature Flows #gr-qc
paper · pdf · doi:10.1088/0264-9381/24/11/f01
published as Class.Quant.Grav.24:F47-F54,2007 · 11 pages, no figures
openalex publication_date 2007/05/09 · arxiv created 2007/11/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Perelman has given a gradient formulation for the Ricci flow, introducing an 'entropy function' which increases monotonically along the flow. We pursue a thermodynamic analogy and apply Ricci flow ideas to general relativity. We investigate whether Perelman's entropy is related to (Bekenstein–Hawking) geometric entropy as familiar from black hole thermodynamics. From a study of the fixed points of the flow, we conclude that Perelman entropy is not connected to geometric entropy. However, we note that there is a very similar flow which does appear to be connected to geometric entropy. The new flow may find applications in black hole physics suggesting, for instance, new approaches to the Penrose inequality.