Pith. sign in

REVIEW 3 major objections 4 minor 58 references

Inconsistencies of nonmetric Einstein-Dirac-Maxwell theories and a cure for geometric flows of f(Q) black ellipsoid, toroid and wormhole solutions

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A nonmetric Einstein-Dirac-Maxwell model shifts fermion masses directionally and generates black ellipsoids, wormholes, and toroids.

desk verdict New nonmetric Einstein-Dirac-Maxwell equations, but the paper's central claim that the displayed metrics are EDM solutions is not supported: the fermion and gauge sectors are never constructed or checked. read the letter →

arxiv 2504.17806 v1 pith:VEWVLONC submitted 2025-04-22 physics.gen-ph

Sergiu I. Vacaru This is my paper · ORCID
classification physics.gen-ph
keywords nonmetricEinstein-Dirac-Maxwellf(Q)gravitynonmetricityanholonomicframedeformationmethodoff-diagonalquasi-stationarysolutionsblackellipsoidwormholeW-entropythermodynamics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper takes on a known obstruction: on a spacetime with a nonmetric connection, the gamma-matrix decomposition of the metric is not preserved by parallel transport, so no unique Dirac operator exists. The proposed cure is to write the nonmetric connection as the metric-compatible connection plus a distortion, working in anholonomic (2+2) dyadic variables, where the nonmetric distortion becomes an extra spin connection and an effective mass term. On that basis the paper formulates a nonmetric Einstein-Dirac-Maxwell (EDM) system, equations (44)--(46) with sources (43), and claims that nontrivial nonmetricity fields $Q$ produce locally anisotropic modifications of fermion mass and act as effective sources in the Maxwell equations. It then generates quasi-stationary off-diagonal solutions describing black ellipsoids, wormholes, and black toroids, with thermodynamics computed from W-entropy functionals rather than standard black-hole surface entropy. If the construction is right, this is a first consistent nonmetric EDM theory with concrete solutions; the paper explicitly leaves the actual spinor and gauge configurations satisfying the matter equations to future work.

What carries the argument

The load-bearing mechanism is the anholonomic frame and connection deformation method, run in (2+2) dyadic variables. Every metric-affine structure is rewritten using a nonlinear connection plus a canonical d-connection, and the nonmetric connection is expressed as $D = \nabla + Z$, the metric-compatible connection plus a distortion. This distortion $Z$ enters the Dirac operator as an extra spin connection ${}_Q\Gamma_\alpha$, the fermion mass as $m_0 + {}_Q M(u)$, and the Maxwell equations as an effective current; all nonmetric, Dirac, and Maxwell contributions are collected into an effective source ${}_Q\hat J_{\alpha\beta}$. In that form the f($Q$) EDM equations decouple into a two-dimensional Poisson equation for the conformal factor and integral equations for the metric and N-connection coefficients, solved by generating functions and effective cosmological constants. The same nonholonomic variables allow W-entropy functionals to define thermodynamic variables for solutions that lack closed horizons.

What would settle it

Take one of the displayed metrics, say the wormhole metric (91), and solve equations (44)--(45) for $\Psi$ and $A$ with the paper's prescribed sources. If no nontrivial regular solutions exist, or if the total source ${}_Q\hat J_{\alpha\beta}$ fails to satisfy the current-conservation identities, those metrics are not genuine EDM solutions. A simpler check: compute ${}_Q M(u)$ for an explicit generating function and see whether a finite, direction-dependent mass shift survives; if it vanishes identically for all allowed generating data, the paper's central physical effect disappears.

Watch

Extended reading notes

Core claim

The paper's central discovery, stated on its own terms, is a worked-out nonmetric EDM system in canonical dyadic variables: a Dirac equation with distorted covariant derivative and mass term $m_0 + {}_Q M(u)$, a Maxwell equation with effective current $j + {}_e j$, and Einstein equations $\hat R_{\alpha\beta} = {}_Q\hat J_{\alpha\beta}$ whose total source combines electromagnetic, Dirac, geometric-distortion, and nonmetric contributions. The paper claims that nontrivial $Q$-fields produce locally anisotropic fermion mass polarizations even in metric-compatible configurations with zero torsion, and that nonmetric electromagnetic sources appear by analogy with classical electrodynamics in anisotropic media. It applies the anholonomic frame and connection deformation method to decouple and integrate these equations, writing solutions in terms of generating functions, effective sources, and effective cosmological constants. Explicit families (84), (91), and (98) are presented as quasi-stationary nonmetric EDM deformations of a rotating cosmological black hole, a wormhole, and a toroidal black hole, respectively, with thermodynamic variables computed from W-entropy rather than surface entropy. The paper does not exhibit the spinor fields $\Psi = B\psi$ and gauge potentials $A$ that would solve (44)--(45) on those metrics; it states that explicit nonmetric deformations of the Dirac--Maxwell fields are deferred to future work.

Load-bearing premise

The construction depends on there being spinor fields $\Psi = B\psi$ and U(1) gauge potentials $A$ that actually solve the nonmetric Dirac-Maxwell equations on the generated metrics; the paper does not construct or check them and states this is left to future work.

Editorial extensions

If this is right

  • If the nonmetric EDM equations (44)--(46) are consistent, the distortion method provides a general decoupling-and-integration scheme, so more off-diagonal nonmetric solution families can be built from the same generating-function construction.
  • A nontrivial $Q$-field changes the effective fermion mass in a direction-dependent way, even in configurations with zero torsion and zero canonical distortion, giving an in-principle observable signature of nonmetricity.
  • The ellipsoidal, wormhole, and toroidal metrics encode nonmetric EDM matter through generating functions and effective sources, so their physical predictions are tied to those sources rather than to an explicit matter action.
  • Because generic quasi-stationary nonmetric EDM solutions lack closed horizons and holographic structure, their thermodynamics must be formulated through W-entropy functionals; standard surface-entropy formulas apply only to restricted subclasses with effective horizon configurations.
  • Small-parameter deformations of the rotating cosmological black hole give black-ellipsoid configurations whose stability can be controlled by nonholonomic constraints.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves open whether any of the displayed metrics actually admits nontrivial spinor and gauge fields; a direct construction of $\Psi$ and $A$ for (84), (91), or (98) would turn the claimed family from ansatz into verified EDM solutions.
  • A testable extension would be to compute ${}_Q M(u)$ explicitly for a chosen generating function and predict direction-dependent fermion-mass shifts; such a calculation is absent here.
  • The consistency of the total source ${}_Q\hat J_{\alpha\beta}$ with the relevant differential conservation identities is not demonstrated; checking it would determine whether the decoupled equations are physically realizable beyond their formal integration.
  • The same distortion machinery is claimed to extend to nonmetric Einstein-Yang-Mills-Higgs systems; if so, the black-ellipsoid and wormhole families become templates for unified nonmetric matter solutions, though the paper supplies no such examples.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript proposes a nonmetric Einstein-Dirac-Maxwell (EDM) theory in canonical nonholonomic variables, based on distortions of the Levi-Civita connection (D = ∇ + Z) and a nonmetric Dirac operator (39). The central equations are the nonmetric Dirac, Maxwell, and Einstein equations (44)-(46), with sources (43) that absorb Dirac-Maxwell distortions. The author applies the anholonomic frame and connection deformation method (AFCDM) to write quasi-stationary off-diagonal solutions generated by functions (64)-(68), and displays three families: nonmetric deformations of Kerr-de Sitter black ellipsoids (84)/(86), wormholes (91)/(92), and toroids (98). He defines generalized Perelman F- and W-functionals (49)-(50) and thermodynamic variables (76)-(79). The paper claims these are the first nonmetric EDM solutions and that nonmetricity induces locally anisotropic fermion masses and effective electromagnetic sources.

Significance. The algebraic construction of off-diagonal metrics from generating functions follows the established AFCDM pattern, and the displayed coefficient formulas (64)-(66) are internally consistent. The idea of using connection distortions to write nonmetric Dirac-type equations is worth exploring, and the explicit refusal to rely on Bekenstein-Hawking thermodynamics in favor of Perelman-type variables is a clear conceptual choice. However, the central claim, that metrics (84), (91), and (98) solve a nonmetric Einstein-Dirac-Maxwell system, is not established: no spinor field Ψ and no gauge potential A are exhibited for any of these metrics, and the matter equations (44)-(45) are never verified. The effective sources (43) and the nonlinear symmetries (70)-(73) are chosen so that the Einstein equations (46)/(73) are satisfied by construction, which makes the gravitational part a prescription rather than a derivation of a coupled matter-gravity solution. If a verification of the Dirac-Maxwell sector were supplied for at least one configuration, the paper would be a substantial contribution; in its present form the advertised results are conditional on an unproved existence statement.

major comments (3)
  1. [3.2.3 (Eqs. (44)-(45) and (75))] The paper never constructs a spinor field Ψ = Bψ or a gauge potential A satisfying the nonmetric Dirac equation (44) and the distorted Maxwell equation (45) for any of the displayed metrics (84), (91), and (98). Section 3.2.3 states that explicit computations of QFαβ and ejβ are 'not the purpose of this work' and that examples of nonmetric deformations of the Dirac-Maxwell equations 'will be studied in future works'; this is a direct admission that the central existence claim is unverified. Since the headline result is the first nonmetric EDM solutions, this omission is load-bearing, not a presentation issue.
  2. [3.2.2 (Eqs. (43) and (70)-(73))] The total source QJ in (43) is defined as the sum of all Dirac-Maxwell, nonmetricity, and distortion terms, and the nonlinear symmetries (70)-(73) are used to choose generating functions so that the ansatz satisfies (73) with effective cosmological constants. This closes the system by absorbing the matter content into the sources; consequently, the construction demonstrates solutions of an effective Einstein equation with prescribed sources, but it does not show that a Dirac-Maxwell configuration realizing those sources exists. This circularity undermines the identification of the metrics as EDM solutions.
  3. [2.3 (Eq. (40))] The nonmetric Dirac equation (44) is postulated with a mass shift QM of the form (40), in which the 4×4 matrix B(u) is left arbitrary. Equation (75) then expresses the mass polarization QM in terms of B without determining B from the Dirac equation; as a result, the claim of locally anisotropic modifications of fermion masses is an ansatz with free parameters rather than a computed effect. The paper itself notes in Section 1.1 that a unique nonmetric Dirac equation requires additional assumptions, but no variational or physical principle is given for the specific choice (40)/(44).
minor comments (4)
  1. [4.2, Eq. (90)] Equation (90) contains an inconsistent integration variable: the text writes 'dθ ϕ whQ J' where 'dϕ whQ J' is evidently intended, and similar typographical errors appear in several displayed formulas in Section 4.2.
  2. [References] Reference [23] misspells Kip Thorne as 'Thorn', and reference [26] contains 'Herldt' instead of the expected 'Herlt'; the reference list should be checked for accuracy.
  3. [Notation] The symbol Q is used both for the nonmetricity tensor Qαβγ and as a left label for Q-deformed objects such as QJ and QΛ, which makes equations like (43) and (72) unnecessarily confusing.
  4. [Abstract and Introduction] The wording 'we prove' is used for statements that are actually algebraic constructions or postulates; the language should be adjusted to 'we construct' or 'we propose' except where a genuine proof is supplied.

Circularity Check

2 steps flagged · score 6.0 of 10

The claimed nonmetric EDM effects are partly self-definitional: the Dirac-Maxwell content is absorbed into freely prescribed effective sources and the arbitrary mass-polarization matrix B, while no Ψ or A is ever checked against eqs. (44)-(45).

  1. self definitional [Sec. 2.3, eq. (43); Sec. 3.2.1-3.2.3, eqs. (64)-(73)]
    "We formulate a nonmetric EDM source by adding DA ˆYαβ + DA Q ˆYαβ (42) and considering a total source QˆJαβ = ˆY[A] αβ + ˆY[D] αβ + Q ˆY[A] αβ + Q ˆY[D] αβ + e Q ˆYβγ (43) ... It is not the purpose of this work to provide tedious technical computations of some explicit Q ˆFαβ(τ ) and ejβ(τ ) because they can be encoded in general form into normalization functions as in (56) and 'dispersed' in off-diagonal terms for corresponding solutions of (73)."

    Equation (46), R̂αβ = QJαβ, is solved by prescribing the generating sources hQJ and vQJ and then constructing the metric through (64)-(66); the nonlinear symmetry (71) enforces R̂βγ = δβγ QΛ(τ). Since the total source QJ is defined as the sum of all nonmetric Dirac-Maxwell distortions, any prescribed source automatically makes the ansatz a solution of the effective gravitational equation. No independent spinor field Ψ or gauge potential A satisfying the actual nonmetric Dirac-Maxwell equations (44)-(45) is exhibited or checked; Sec. 3.2.3 explicitly defers those computations to future work. Thus the label 'nonmetric EDM solution' reduces to a choice of source functions rather than to verified matter-field configurations.

  2. fitted input called prediction [Sec. 2.3, eqs. (40)-(41); Sec. 3.2.3, eq. (75)]
    "m0 → M (u) = m0 + QM (u), for Ψ = B(u) ψ computed as a 4 × 4 matrix for any fixed point values, when QM = −i ℏ γα QˆΓα +m0B − 3/2 ℏ 3 ˆTαγαγ5. ... jβ := Ψ γβ Ψ = ˆjβ + ejβ, for a respective parametrization of B(u) which allow us to represent ˆjβ := ψ γβψ and additional Q-deformations resulting in ejβ."

    The claimed locally anisotropic mass modification QM contains the term m0B, where B is an arbitrary 4×4 matrix that is never fixed by any equation or Lagrangian. By choosing B, one can produce any desired mass polarization, so this is a free parametrization rather than a derived prediction. Similarly, the nonmetric induced electromagnetic source ejβ is defined as the difference between ΨγβΨ and ψγβψ after a suitable choice of B; it is a bookkeeping identity, not an independently computed effect. The paper itself states that explicit QFαβ and ejβ computations are not the purpose of the work and defers the nonmetric Dirac-Maxwell equations to future works.

full rationale

The paper has a genuine, non-circular core: given arbitrary effective sources hQJ and vQJ, the AFCDM formulas (64)-(66) generate off-diagonal metrics satisfying the effective Einstein-type equation (73)/(46), and this construction is internally consistent. The circularity appears when these metrics are advertised as nonmetric EDM solutions and when nontrivial Q-fields are said to modify fermion masses and Maxwell sources. The total source (43) is defined to include all Dirac-Maxwell and nonmetric distortions, and the actual Dirac/Maxwell fields are never constructed or verified: Sec. 3.2.3 explicitly leaves QFαβ and ejβ uncomputed and defers the Dirac-Maxwell equations to future work. The mass shift (40)/(75) contains the free matrix B, so the 'locally anisotropic mass polarization' is not a prediction but a parametrization; similarly ejβ is fixed by the choice of B. Because the gravitational ansatz remains an honest effective-source solver and would become a genuine EDM solution if explicit Ψ and A satisfying (44)-(45) were supplied, the circularity is partial rather than total. Score 6.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The constructed solutions depend on arbitrary generating functions, integration functions, effective cosmological constants, and a mass-polarization matrix B. The field equations and Perelman functionals are postulated or taken from the author's prior work. No new particles or forces are introduced.

free parameters (4)
  • generating functions JPhi, Phi, eta4, zeta4, chi4 = arbitrary functions
    All constructed quasi-stationary metrics are expressed through these free functions; they determine the solutions and can be chosen at will.
  • effective cosmological constants QLambda(tau) = [hLambda, vLambda] = not fixed
    Introduced through nonlinear symmetries (71)-(72) and used to compute all thermodynamic variables, but never predicted from the theory.
  • integration functions g4[0], 1n_k, 2n_k = arbitrary functions
    Free functions appearing in the general ansatz (66)-(68); they affect the explicit form of every constructed solution.
  • mass polarization matrix B(u) = unspecified
    The nonmetric fermion mass shift in (75) depends on an arbitrary 4x4 matrix B chosen so that Psi = B psi is a solution; no explicit B is derived.
assumptions (5)
  • domain assumption The f(Q) gravitational equations in canonical nonholonomic variables, Eqs. (24)-(25), are taken as the starting point.
    Borrowed from the author's partner work [21]; not re-derived in this paper.
  • domain assumption The canonical d-connection D-hat with zero h/v torsion but nonzero hv torsion is a valid alternative to the Levi-Civita connection for constructing physical solutions.
    Solutions are generated for the D-hat equations (30) and only conditionally reduced to LC solutions by setting T = 0, as noted in Sec. 2.1.4.
  • ad hoc to paper The nonmetric Dirac equation (44) is postulated with a mass shift QM of the form (40).
    No variational derivation is provided, and the shift depends on an arbitrary B matrix.
  • ad hoc to paper The modified Perelman functionals (49)-(50) and thermodynamic variables (61) are postulated for nonmetric EDM flows.
    They are asserted as generalizations of Perelman's functionals without derivation.
  • domain assumption The chosen 2+2 nonholonomic splitting and AFCDM ansatz (63) can represent a general class of nonmetric EDM solutions.
    The method restricts to quasi-stationary metrics with Killing symmetry on the time-like coordinate.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Inconsistencies of nonmetric Einstein-Dirac-Maxwell theories and a cure for geometric flows of f(Q) black ellipsoid, toroid and wormhole solutions." pith.science (2026). https://pith.science/paper/VEWVLONC

@misc{pith2026250417806,
  author       = {Pith},
  title        = {Pith review of: Inconsistencies of nonmetric Einstein-Dirac-Maxwell theories and a cure for geometric flows of f(Q) black ellipsoid, toroid and wormhole solutions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VEWVLONC}},
  note         = {Machine review of arXiv:2504.17806}
}
read the original 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.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

58 extracted references · 36 canonical work pages

  1. [22]

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

    L. Bubuianu, J. O. Seti, S. Vacaru, E. V. Veliev, Nonassoc iative Einstein–Dirac–Maxwell systems and R-flux modified Reissner–Nordström black holes and wormhole s, Gen. Rel. Grav. 56 (2024) 80, arXiv: 2410.03701

    work page Pith review arXiv 2024

  2. [17]

    M. Adak, T. Dereli and L. H. Ryder, Dirac equation in spac etimes with torsion and non-metricity, Int. J. Mod. Phys. D12 (2003) 145-156, arXiv: gr/0208042

    work page arXiv 2003

  3. [19]

    Non-metricities, torsion and fermions

    G. de Berredo-Peixoto, Non-metricities, torsion and fe rmions, arXiv: 1807.03270v2

    work page Pith review arXiv

  4. [1]

    Gravitation and Electricity

    H. Weyl, Gravitation und Elektriticitat, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1918 (1918) 465; English tranlation as "Gravitation and Electricity" i n: The Principle of Relativity (Dover, NY, 1952)

    work page 1918

  5. [2]

    F. W. Hehl, J. D. McCrea, E. W. Mielke, and Y. Ne’eman, Metr ic-affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breakin g of dilaton invariance, Phys. Rept. 258 (1995) 1-171; arXiv: gr-qc/9402012

    arXiv 1995

  6. [4]

    Heisenberg, Review on f(Q) gravity, Phys

    L. Heisenberg, Review on f(Q) gravity, Phys. Rept. 1066 ( 2024) 1-78, arXiv: 2309.15958

    arXiv 2024

  7. [5]

    Critical Remarks on Finsler Modifications of Gravity and Cosmology by Zhe Chang and Xin Li

    S. Vacaru, Critical remarks on Finsler modifications of g ravity and cosmology by Zhe Chang and Xin Li, Phys. Lett. B 690 (2010) 224-228; arXiv: 1003.0044v2

    work page Pith review arXiv 2010

  8. [6]

    Metric Compatible or Noncompatible Finsler-Ricci Flows

    S. Vacaru, Metric compatible or noncompatible Finsler- Ricci flows, Int. J. Geom. Meth. Mod. Phys. 9 (2012) 1250041; arXiv: 1106.4888

    work page Pith review arXiv 2012

Show all 58 references
  1. [7]

    Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv: math

    G. Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv: math. DG/0211159

  2. [8]

    R. S. Hamilton, Three-manifolds with positive Ricci cur vature, J. Diff. Geom. 17 (1982) 255-306

    1982

  3. [9]

    Vacaru, Nonholonomic Ricci flows: II

    S. Vacaru, Nonholonomic Ricci flows: II. Evolution equat ions and dynamics, J. Math. Phys. 49 (2008) 043504; arXiv: math.DG/0702598

    2008

  4. [10]

    Harko, N

    T. Harko, N. Myrzakulov, R. Myrzakulov and S. Shahidi, N on-minimal geometry-matter coupling in Weyl- Cartan space-tiems: f(R,T,Q,Tm) gravity, Physics of the Da rk Universe 34 (2021) 100886

    2021

  5. [11]

    Iosifidis, R

    D. Iosifidis, R. Myrzakulov, L. Ravera, G. Yergaliyeva, and K. Yerzhanov, Metric-affine vector-tensor correspondence and implications in F(R,T,Q, T,D ) gravity, Physics of the Dark Universe 37 (2022) 101094 36

    2022

  6. [12]

    Khyllep, J

    W. Khyllep, J. Dutta, E. Saridakis, and K. Yesmakhanova , Cosmology in f(Q) gravity: A unified dynamical systems analysiso of the background and perturbations, Phy s. Rev. D 107 (2023) 044022; arXiv: 2207.02610

    2023 arXiv

  7. [13]

    D. M. Ghilencea, Non-metric geometry as the origing of m ass in gauge theories of scale invariance, Eur. Phys. J. C 83 (2023) 176; arXiv: 2203.05381

    2023 arXiv

  8. [14]

    Koussour and A vik De, Observational contraints on tw o cosmological models of f (Q) theory, Eur

    M. Koussour and A vik De, Observational contraints on tw o cosmological models of f (Q) theory, Eur. Phys. J. C 83 (2023) 400; arXiv: 2304.11765

    2023 arXiv

  9. [15]

    Zhao, Covariant formulation of f(Q) theory, Eur

    D. Zhao, Covariant formulation of f(Q) theory, Eur. Phy s. J. C 82 (2022) 303; arXiv: 2104.02483

    2022 arXiv

  10. [16]

    De and T

    A. De and T. H. Loo, On the viability of f(Q) gravity model s, Class. Quantum. Grav. 40 (2023) 115007, arXiv: 2212.08304

    2023 arXiv

  11. [18]

    J. B. Formiga and C. Romero, Dirac equation in non-Rieman nian geometries, Int. J. Geom. Meth. Mod. Physics, 10 (2013) 1320012, arXiv: 1210.1615v2

    2013 arXiv

  12. [20]

    Bubuianu, S

    L. Bubuianu, S. Vacaru, E. V. Veliev and A. Zhamysheva, Da rk energy and dark matter configurations for womholes and solitonic heararchies of nonmetric Ricci flows and F (R,T,Q,T m) gravity, Eur. Phys. J. C 84 (2024) 211; arXiv 2402.19362

    2024 arXiv

  13. [21]

    Bubuianu, E

    L. Bubuianu, E. Nurlan, J. O. Seti, S. Vacaru, E. V. Veliev , Nonmetric geometric flows and quasicrystalline topological phases for dark energy and dark matter in f(Q) co smology, Eur. Phys. J. C 84 (2024) 653, arXiv: 2410.03700

    2024 arXiv

  14. [23]

    C. W. Misner, K. S. Thorn and J. A. Wheeler, Gravitation ( Freeman, 1973)

    1973

  15. [24]

    S. W. Hawking and C.F. R. Ellis, The Large Scale Structur e of Spacetime (Cambridge University Press, 1973)

    1973

  16. [25]

    R. W. Wald, General Relativity (Universtiy of Chicago P ress, Chicago, IL, 1984)

    1984

  17. [26]

    Kramer, H

    D. Kramer, H. Stephani, E. Herdlt, and M. A. H. MacCallum , Exact Solutions of Einstein’s Field Equations, 2d edition (Cambridge University Press, 2003)

    2003

  18. [27]

    Bubuianu and S

    L. Bubuianu and S. Vacaru, Deforming black hole and cosmo logical solutions by quasiperiodic and/or pat- tern forming structures in modified and Einstein gravity, Eu r. Phys. J. C 78 (2018) 393; arXiv: 1706.02584

    2018 arXiv

  19. [28]

    S. Vacaru, On axiomatic formulation of gravity and matt er field theories with MDRs and Finsler-Lagrange- Hamilton geometry on (co) tangent Lorentz bundles, arXiv: 1 801.06444; published without historical remarks as: L. Bubuianu and S. Vacaru, Axiomatic formulation s of modifie...

    2018

  20. [29]

    Vacaru, Geometric information flows and G

    S. Vacaru, Geometric information flows and G. Perelman e ntropy for relativistic classical and quantum mechanical systems, Eur. Phys. J. C 80 (2020) 639; arXiv: 190 5.12399 37

    2020

  21. [30]

    J. D. Bekenstein, Generalized second law of thermodynam ics in black hole physics, Phys. Rev. D 9 (1974) 3292-3300

    1974

  22. [31]

    S. W. Hawking, Black holes and thermodynamics, Phys. Rev . D 13 (1976) 191-197

    1976

  23. [32]

    Cabral, F

    F. Cabral, F. S. N. Lobo and D. Rubiera-Garcia, Imprints from a Riemann-Cartan space-time on the energy levels of Dirac spinors. Class. Quant. Grav. 38 (2021 ) 19, 195008; arXiv: 2102.02048

    2021 arXiv

  24. [33]

    H. -D. Cao and H. -P. Zhu, A complete proof of the Poincaré and geometrization conjectures - application of the Hamilton–Perelman theory of the Ricci flow, Asian J. Ma th. 10 (2006) 165-495

    2006

  25. [34]

    J. W. Morgan and G. Tian, Ricci flow and the Poincaré conje cture, AMS, Clay Math.Monog. v.3 (2007)

    2007

  26. [35]

    Kleiner and J

    B. Kleiner and J. Lott, Notes on Perelman’s papers, Geome try & Topology 12 (2008) 2587-2855

    2008

  27. [36]

    Friedan, Nonlinear models in 2 +ε dimensions, Phys

    D. Friedan, Nonlinear models in 2 +ε dimensions, Phys. Rev. Lett. 45 (1980) 1057 -1060

    1980

  28. [37]

    Friedan, Ricci flows

    D. Friedan, Ricci flows. Nonlinear models in 2 +ε dimensions, Annals of Physics, NY, 163 (1985) 318-419

    1985

  29. [38]

    Vacaru, Anholonomic soliton-dilaton and black hole solutions in general relativity, JHEP, 04 (2001) 009; arXiv: gr-qc/0005025

    S. Vacaru, Anholonomic soliton-dilaton and black hole solutions in general relativity, JHEP, 04 (2001) 009; arXiv: gr-qc/0005025

    2001 arXiv

  30. [39]

    Vacaru and F

    S. Vacaru and F. C. Popa, Dirac spinor waves and solitons in anisotropic Taub-NUT spaces, Class. Quant. Gravity, 18 (2001) 4921-4938; arXiv: hep-th/0105316

    2001 arXiv

  31. [40]

    Vacaru and D

    S. Vacaru and D. Singleton, Warped solitonic deformati ons and propagation of black holes in 5D vacuum gravity, Class. Quant. Grav. 19 (2002) 3583-3602; arXiv: he p-th/0112112

    2002

  32. [41]

    Vacaru and D

    S. Vacaru and D. Singleton, Ellipsoidal, cylindrical, bipolar and toroidal wormholes in 5D gravity, J. Math. Phys. 43 (2002) 2486-2504; arXiv: hep-th/0110272

    2002 arXiv

  33. [42]

    Vacaru, Finsler black holes induced by noncommutati ve anholonomic distributions in Einstein gravity, Class

    S. Vacaru, Finsler black holes induced by noncommutati ve anholonomic distributions in Einstein gravity, Class. Quant. Grav. 27 (2010) 105003; arXiv: 0907.4278

    2010 arXiv

  34. [43]

    Bubuianu and S

    L. Bubuianu and S. Vacaru, Black holes with MDRs and Bekenst ein-Hawking and Perelman entropies for Finsler-Lagrange-Hamilton spaces, Annals of Physics, NY, 404 (2019) 10-38; arXiv: 1812.02590

    2019 arXiv

  35. [44]

    Bubuianu, S

    L. Bubuianu, S. Vacaru and E. V. Veliev, Nonassociative b lack ellipsoids distorted by R-fluxes and four dimensional thin locally anisotropic accretion disks, Eur . Phys. J. C 81 (2021) 1145; arXiv: 2108.04689

    2021 arXiv

  36. [45]

    Bubuianu, D

    L. Bubuianu, D. Singleton, and S. Vacaru, Nonassociativ e black holes in R-flux deformed phase spaces and relativistic models of G. Perelman thermodynamics, JHEP 05 (2023) 057; arXiv: 2207.05157

    2023 arXiv

  37. [46]

    Ovalle, E

    J. Ovalle, E. Contrera and Z. Stuchlik, Ker-de Sitter bl ack hole revisited, Phys. Rev. D 103 (2021) 084016, arXiv: 2104.06359

    2021 arXiv

  38. [47]

    d’Abrosio, S

    F. d’Abrosio, S. D. B. Fell, L. Heisenberg and S.Kuhn, Blac k holes in f(Q) gravity, Phys. Rev. D 105 (2022) 024042, arXiv: 2109.03174

    2022 arXiv

  39. [48]

    Vacaru, Wormholes and off-diagonal solutions in f(R, T), Einstein and Finsler gravity theories, in: (eds.) A

    S. Vacaru, Wormholes and off-diagonal solutions in f(R, T), Einstein and Finsler gravity theories, in: (eds.) A. Garcia-Parrado, F. C. Mena, F. Moura. E. Vaz, Pr ogress in Mathematical Rela- tivity, Gravitation and Cosmology, Springer Proceedings i n Mathematics & Statistics, 6...

    2014 arXiv

  40. [49]

    Vacaru, Exact solutions in modified massive gravity a nd off-diagonal wormhole deformations, Eur

    S. Vacaru, Exact solutions in modified massive gravity a nd off-diagonal wormhole deformations, Eur. Phys. J. C 74 (2014) 2781; arXiv: 1403.1815

    2014 arXiv

  41. [50]

    M. S. Morris and K. S. Thorne, Wormhole in spacetime and t heir use for interstellar travel: a tool for teaching general relativity, Am. J. Phys. 56 (1988) 395-412

    1988

  42. [51]

    S. Kar, S. N. Minwalla, D. Mishra and D. Sahdev, Resonanc es in the transmission of massless scalar waves in a class of wormholes, Phys. Rev. D 51 (1994) 1632-1638

    1994

  43. [52]

    P. D. Roy, S. Aneesh, and S. Kar, Revisiting a family of wo rmholes: geometry, matter, scalar quasinormal modes and echoes, Eur. Phys. J. 80 (2020) 850, arXiv: 1910.08 746

    2020

  44. [53]

    T. F. de Souza, A. C. A Ramos, R. N. Costa Filho and J. Furta do, Generalized Ellis-Bronnikov graphene wormhole, arXiv: 2208.06869

    arXiv

  45. [54]

    Vacaru, Black tori in Einstein and 5D gravity, hep-th/ 0110284; Chapter 11 in: Clifford and Riemann- Finsler Structures in Geometric Mechanics and Gravity, Sel ected Works, by S

    S. Vacaru, Black tori in Einstein and 5D gravity, hep-th/ 0110284; Chapter 11 in: Clifford and Riemann- Finsler Structures in Geometric Mechanics and Gravity, Sel ected Works, by S. Vacaru, P. Stavrinos, E. Gaburov and D. Gonta. Differential Geometry - Dynamical Syst ems, Monogr...

    2006 arXiv

  46. [55]

    J. P. S. Lemos, Supersymmetry of the extreme rotating to roidal black hole, Nucl. Phys. B 600 (2001) 272-284, arXiv: hep-th/0011234

    2001 arXiv

  47. [56]

    C. S. Peca, J. P. S. Lemos, Thermodynamics of toroidal bl ack holes, J. Math. Phys. 41 (2000) 4783-4789, arXiv: gr-qc/9809029

    2000 arXiv

  48. [57]

    Emparan and H

    R. Emparan and H. S. Reall, A rotating black ring solutio n in five-dimenions, Phys. Rev. Lett. 88 (2002) 101101, arXiv: hep-th/0110260

    2002 arXiv

  49. [58]

    Emparan and H

    R. Emparan and H. S. Real, Black holes in higher dimension , Living Rev. Rel. 11 (2008) 6, arXiv: 0801.3471

    2008 arXiv

  50. [59]

    Astorino, F

    M. Astorino, F. Canfora, A. Giacomini and M. Ortaggio, H airy AdS black holes with a toroidal horizon in 4D Einstein-nonlinear σ-model system, Phys. Lett. B776 (2018) 236-241; arXiv: 1711. 08100 39

    2018

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.