Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows

Autor: Sergiu I. Vacaru, Elşen Veli Veliev, Laurenţiu Bubuianu
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: European Physical Journal C: Particles and Fields, Vol 81, Iss 1, Pp 1-25 (2021)
Druh dokumentu: article
ISSN: 1434-6044
1434-6052
DOI: 10.1140/epjc/s10052-020-08798-8
Popis: 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.
Databáze: Directory of Open Access Journals
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