2019/04/30 by Sergiu I. Vacaru, Elşen Veli Veliev, Laurenţiu Bubuianu · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #Entropic gravity #Entropy (arrow of time) #General relativity #Geometric Analysis and Curvature Flows #Gravitation #Gravitational field #Nonholonomic system #Nonlinear system #Parametric statistics #Spacetime #msc:35Q75 #msc:37D35 #msc:37J60 #msc:53C44 #msc:53C50 #msc:53C80 #msc:82D99 #msc:83C15 #msc:83C55 #msc:83C99 #msc:83D99 #physics.gen-ph
paper · pdf · doi:10.1140/epjc/s10052-020-08798-8
published as Eur. Phys. J. C 81 (2021) 81 · accepted to EPJC; latex2e 11pt, 35 pages with a table of contents; v3 is substantially modified with a new title and a new co-author
arxiv created 2020/12/23 · openalex publication_date 2021/01/01 · openalex created_date 2021/01/05 · arxiv updated 2021/01/29 · openalex updated_date 2026/08/05
Abstract We develop an approach to the theory of relativistic geometric flows and emergent gravity defined by entropy functionals and related statistical thermodynamics models. Nonholonomic deformations of G. Perelman’s functionals and related entropic values used for deriving relativistic geometric evolution flow equations. For self-similar configurations, such equations describe generalized Ricci solitons defining modified Einstein equations. We analyse possible connections between relativistic models of nonholonomic Ricci flows and emergent modified gravity theories. We prove that corresponding systems of nonlinear partial differential equations, PDEs, for entropic flows and modified gravity posses certain general decoupling and integration properties. There are constructed new classes of exact and parametric solutions for nonstationary configurations and locally anisotropic cosmological metrics in modified gravity theories and general relativity. Such solutions describe scenarios of nonlinear geometric evolution and gravitational and matter field dynamics with pattern-forming and quasiperiodic structure and various space quasicrystal and deformed spacetime crystal models. We analyse new classes of generic off-diagonal solutions for entropic gravity theories and show how such solutions can be used for explaining structure formation in modern cosmology. Finally, we speculate why the approaches with Perelman–Lyapunov type functionals are more general or complementary to the constructions elaborated using the concept of Bekenstein–Hawking entropy.