Nonassociative Einstein-Dirac-Maxwell systems and R-flux modified Reissner-Nordstr\"om black holes and wormholes

TL;DR

This paper develops a nonassociative and noncommutative Einstein-Dirac-Maxwell model inspired by string theory, providing exact solutions for deformed black holes and wormholes, and exploring their thermodynamic properties beyond traditional entropy concepts.

Contribution

It introduces a novel nonassociative geometric framework for Einstein-Dirac-Maxwell systems, deriving exact solutions for deformed black holes and wormholes in phase space.

Findings

Exact nonassociative deformations of Reissner-Nordström black holes

Construction of nonassociative phase space wormholes with fermions

Proposal of modified thermodynamic variables for nonassociative objects

Abstract

We elaborate on a model of nonassociative and noncommutative Einstein--Dirac-Maxwell, EDM, theory determined by star product R-flux deformations in string theory. Solutions for nonassociative EDM systems and physical properties not studied in modern physics. For modifications of the four-dimensional, 4-d, Einstein gravity, we work on conventional nonassociative 8-d phase spaces modelled as star-deformed co-tangent Lorentz bundles. Generalizing the anholonomic frame and connection deformation method, the nonassociative EDM equations are decoupled and integrated in exact and parametric quasi-stationary forms. Corresponding generic off-diagonal metrics are described by nonlinear symmetries and encode nonassociative effective sources and generating functions depending on space and momentum-like coordinates. For respective nonholonomic parameterizations, such solutions describe nonassociative deformations of the Reissner-Nordstr\"{o}m black holes. A variant of nonassociative phase space wormhole solution with fermions possessing anisotropic polarized masses is also analyzed. We conclude that such phase space physical objects can't be characterized using the concept of Bekenstein-Hawking entropy and show how to compute another type (modified G. Perelman ones) nonassociative geometric and statistical thermodynamic variables.