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 studying 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 generalisation of f(Q) gravity. We develop our anholonomic frame and connection deformation method, which allows us to decouple in a general form and integrate nonmetric gravitational and matter field 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 parameterisations, such solutions describe nonmetric EDM deformations of BH and cosmological metrics. Variants of nonmetric BH, WH and toroid solutions with locally anisotropic polarisations of the gravitational vacuum, masses of fermions, and effective electromagnetic sources are constructed and analysed. Such nonmetric deformed physical objects can't be characterised in the framework of the Bekenstein-Hawking paradigm if certain effective horizon/ holographic configurations are not involved. We show how to define and compute other types of nonmetric geometric thermodynamic variables using generalisations of the concept of G. Perelman W-entropy.

latex2e 11pt, 39 pages with a table of contents, version 2 equivalent to that published online: Fortschr. Phys. 2025, e70003

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Cited by in corpus (2)

• Off-diagonal solutions in Einsteingravity modeling f(R) gravity and dynamical darkenergy vs Lambda CDM cosmology
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations