Inconsistencies of Nonmetric Einstein–Dirac–Maxwell Theories and a Cure for Geometric Flows of f(Q) Black Ellipsoid, Toroid, and Wormhole Solutions

Abstract

Many papers on modified gravity theories (MGTs), and metric-affine geometry have been published. New classes of black hole (BH), wormhole (WH), and cosmological solutions involving nonmetricity and torsion fields were constructed. Nevertheless, the fundamental problems of formulating nonmetric Einstein–Dirac–Maxwell (EDM), equations, and study of important nonmetric gravitational, electromagnetic and fermion effects, have not been solved in MGTs. The main goal of this work is to elaborate on a model of nonmetric EDM theory as a generalization of f(Q) gravity. The authors developed anholonomic frame and connection deformation method which allowed authors to decouple in general form and integrate nonmetric gravitational and matter fields equations. New classes of generated quasi-stationary solutions are defined by effective sources with Dirac and Maxwell fields, nonmetricity and torsion fields, and generating functions depending, in general, on all space-time coordinates. For respective nonholonomic parameterizations, such solutions describe nonmetric EDM deformations of BH and cosmological metrics. Variants of nonmetric BH, WH, and toroid solutions with locally anisotropic polarizations of the gravitational vacuum and masses of fermions, and effective electromagnetic sources, are constructed and analyzed. Such nonmetric deformed physical objects cannot be characterized in the framework of the Bekenstein–Hawking paradigm if certain effective horizon/holographic configurations are not involved. It is shown how to define and compute other types of nonmetric geometric thermodynamic variables using generalizations of the concept of G. Perelman W-entropy.