Nonassociative black holes in R-flux deformed phase spaces and relativistic models of G. Perelman thermodynamics

Abstract

This paper systematically explores new classes of black hole (BH) solutions in nonassociative and noncommutative gravity by focusing on features that generalize to higher dimensions. The theories we study are modelled on (co) tangent Lorentz bundles (i.e. eight dimensional phase spaces) with a star product structure determined by R-flux deformations in string theory. The nonassociative vacuum Einstein equations involve real and complex effective sources with coefficients which are proportional to the Planck and string constants or their products. We develop the anholonomic frame and connection deformation method and prove that such systems of nonlinear partial differential equations can be decoupled and integrated in general form for a generic off-diagonal ansatz for symmetric and non-symmetric metrics. The coefficients of such metrics may depend on all phase space coordinates (space-time coordinates plus energy-momentum). Conditions are given when the generating and integration functions and effective sources define two classes of physically important exact and parametric solutions with R-flux sources related via nonlinear symmetries to effective cosmological constants: (1) 6D Tangherlini BHs, which are star product and R-flux distorted to quasi-stationary configurations and 8D black ellipsoids (BEs) and BHs; (2) nonassocitative space-time and co-fiber space double BH and/or BE configurations generalizing Schwarzschild - de Sitter metrics. We argue that the concept of Bekenstein-Hawking entropy is applicable only for very special classes of nonassociative BHs encoding conventional horizons and (anti) de Sitter configurations. Finally, we show how analogs of the relativistic G. Perelman geometric thermodynamic variables can be defined and computed for general classes of off-diagonal solutions encoding nonassociative R-flux deformations.

arXiv commentlatex2e, 11pt, 38 pages; v2 modified following editor/referee's request and accepted by JHEP

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• The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories
• Nonassicative cosmological solitonic R-flux deformations in gauge gravity and G. Perelman geometric flow thermodynamics
• Nonassociative Einstein-Dirac-Maxwell systems and R-flux modified Reissner-Nordström black holes and wormholes
• Nonmetric geometric flows and quasicrystalline topological phases for dark energy and dark matter in $f(Q)$ cosmology
• Raychaudhuri equations, Tidal forces and Weak field Limit in Schwarzshild-Finsler-Randers spacetime
• Inconsistencies of nonmetric Einstein-Dirac-Maxwell theories and a cure for geometric flows of f(Q) black ellipsoid, toroid and wormhole solutions
• Asymptotic safe nonassociative quantum gravity with star R-flux products, Goroff-Sagnotti counter-terms, and geometric flows
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations