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.

arXiv commentlatex2e 11pt, 39 pages with a table of contents, version 2 equivalent to that published online: Fortschr. Phys. 2025, e70003

References in corpus (38)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• A rotating black ring in five dimensions
• Black Holes in Higher Dimensions
• Notes on Perelman's papers
• Covariant formulation of f(Q) theory
• Black holes in $f(\mathbb{Q})$ Gravity
• Cosmology in $f(Q)$ gravity: A unified dynamical system analysis at background and perturbation levels
• Observational constraints on two cosmological models of $f(Q)$ theory
• Kerr-de Sitter Black Hole Revisited
• Nonholonomic Ricci Flows: II. Evolution Equations and Dynamics
• Anholonomic Soliton-Dilaton and Black Hole Solutions in General Relativity
• On the viability of $f(Q)$ gravity models
• Thermodynamics of toroidal black holes
• Ellipsoidal, Cylindrical, Bipolar and Toroidal Wormholes in 5D Gravity
• Finsler Black Holes Induced by Noncommutative Anholonomic Distributions in Einstein Gravity
• Non-metric geometry as the origin of mass in gauge theories of scale invariance
• Critical Remarks on Finsler Modifications of Gravity and Cosmology by Zhe Chang and Xin Li
• Non-minimal geometry-matter couplings in Weyl-Cartan space-times: $f(R,T,Q,T_m)$ gravity
• Dirac Spinor Waves and Solitons in Anisotropic Taub-NUT Spaces
• Warped Solitonic Deformations and Propagation of Black Holes in 5D Vacuum Gravity
• Black Holes with MDRs and Bekenstein-Hawking and Perelman Entropies for Finsler-Lagrange-Hamilton Spaces
• Deforming Black Hole and Cosmological Solutions by Quasiperiodic and/or Pattern Forming Structures in Modified and Einstein Gravity
• Hairy AdS black holes with a toroidal horizon in 4D Einstein-nonlinear $\sigma$-model system
• Exact Solutions in Modified Massive Gravity and Off-Diagonal Wormhole Deformations
• Dirac equation in spacetimes with torsion and non-metricity
• Geometric information flows and G. Perelman entropy for relativistic classical and quantum mechanical systems
• Supersymmetry of the extreme rotating toroidal black hole
• Metric-Affine Vector-Tensor Correspondence and Implications in $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity
• Imprints from a Riemann-Cartan space-time on the energy levels of Dirac spinors
• Nonassociative black holes in R-flux deformed phase spaces and relativistic models of G. Perelman thermodynamics
• Metric Compatible or Noncompatible Finsler-Ricci Flows
• Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and $F(R,T,Q,T_m)$ gravity
• Search for Missing Links Between Two Extreme Wind Speed Profiles : Dark Energy Accretion and Adiabatic Fluid Accretion
• Nonassociative black ellipsoids distorted by R-fluxes and four dimensional thin locally anisotropic accretion disks
• Wormholes and Off-Diagonal Solutions in f(R,T), Einstein and Finsler Gravity Theories
• Dirac equation in non-Riemannian geometries
• 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

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