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Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows by Vacaru, Sergiu I.; Veliev, Elşen Veli; Bubuianu, Laurenţiu is a scholarly article available to read on EtoBox.

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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 are used for deriving relativistic geometric evolution flow equations. For self-similar configurations, such equations describe generalized Ricci solitons defining modified Einstein equations. We analyze 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 possess 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 analyz

Author

Vacaru, Sergiu I.; Veliev, Elşen Veli; Bubuianu, Laurenţiu

Published

2019

Language

EN