Pith. sign in

REVIEW 3 major objections 5 minor 60 references

Non-metricity effects on electron scattering in bumblebee gravity

T0 review · 3 major / 5 minor · reviewed 2026-07-14 · grok-4.5

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

Pith's one-line read Non-metricity in metric-affine bumblebee gravity rescales Coulomb scattering for a timelike vacuum and adds a quadrupolar anisotropy for a spacelike vacuum, with atomic data bounding the Lorentz-violating parameter.

desk verdict Clean isotropic-vs-quadrupolar split from the metric-affine bumblebee propagator; the electron Born step is the soft link, not the algebra. read the letter →

arxiv 2603.15959 v2 pith:ZMD5DDMB submitted 2026-03-16 gr-qc hep-th

A. A. Araújo Filho This is my paper · ORCID
classification gr-qchep-th
keywords metric-affinebumblebeegravitynon-metricityLorentzviolationelectronscatteringRutherfordcrosssectionquadrupolarpotentialhydrogenspectroscopy
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 asks how the non-metric geometry that appears when Lorentz symmetry is spontaneously broken by a vector field changes the way electrons scatter. In the metric-affine version of bumblebee gravity the independent connection can be integrated out, leaving an effective propagator for the vector fluctuations whose poles are shifted by non-metricity. When the vacuum expectation value is purely timelike the shift is isotropic: the static potential remains Coulombic but with a uniformly rescaled strength, so Rutherford scattering keeps its classic angular shape and the Lorentz-violating parameter appears only as an overall factor. When the vacuum is spacelike the dispersion becomes direction-dependent; the potential acquires an isotropic piece plus a quadrupolar modulation proportional to the second Legendre polynomial of the angle between the separation vector and the preferred axis. That angular structure survives in the differential and transport cross sections while the long-range 1/r tail is preserved. Atomic spectroscopy and clock-comparison experiments then translate these corrections into concrete limits on the product of the non-metricity coupling and the vacuum expectation value, with the anisotropic channel yielding the tighter bounds.

What carries the argument

The pole condition A(k) = 0 of the full momentum-space bumblebee propagator, which supplies the static Green kernel G(k) and, after Fourier transform, the interparticle potential used in the first-order Born scattering amplitude.

What would settle it

A precision measurement of orientation-dependent or sidereal modulations in the magnetic-sublevel splittings of hydrogenic p-states (or clock-comparison transitions) at fractional levels below a few times 10^{-15} that either matches or rules out the predicted quadrupolar shift proportional to ξ b^{2}.

Watch

Extended reading notes

Core claim

Non-metricity induced by a bumblebee vacuum expectation value modifies the static Green function of the vector fluctuations so that a timelike background only rescales the Coulomb coupling while a spacelike background produces an orientation-dependent potential V(r,α̂) ≈ (1/4πr)[1 + ξ b^{2}/6 + (ξ b^{2}/3)P_{2}(cos α̂)]. The resulting electron scattering amplitudes therefore retain Rutherford forward peaking but become anisotropic in the spacelike case, and atomic data constrain |ξ b^{2}| at the 10^{-10}–10^{-11} level isotropically and potentially 10^{-15}–10^{-18} for the quadrupolar term.

Load-bearing premise

The static Green function taken from the free bumblebee propagator is assumed to be the effective potential felt by a nonrelativistic electron, without a derived electron–bumblebee vertex from the matter sector.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper studies electron scattering in metric-affine bumblebee gravity after integrating out the independent affine connection. Non-metricity modifies the bumblebee fluctuation propagator: a timelike VEV yields an isotropic Coulomb potential with overall factor 1/(1+ξb²/2) and Rutherford scattering rescaled only in magnitude, while a spacelike VEV produces an anisotropic static Green function with isotropic plus P₂(cos α̂) quadrupolar pieces. These structures are propagated into Born, Mott, eikonal, and transport cross sections, and order-of-magnitude atomic bounds on ξb² are extracted from hydrogen spectroscopy (isotropic) and anisotropy/sidereal searches (quadrupolar).

Significance. If the identification of the free bumblebee Green function with the electron interparticle potential is justified, the work would give a concrete, falsifiable phenomenological window on metric-affine non-metricity, with a clean isotropic-versus-quadrupolar dichotomy and distinctive directional signatures in differential cross sections. Strengths include a careful weak-field propagator inversion and pole analysis, a closed-form anisotropic potential obtained by rescaling the Poisson operator, and a systematic treatment of IR-regulated total and transport cross sections plus Mott/eikonal checks. The spacelike quadrupolar bounds are in principle more robust than pure coupling rescalings because they cannot be absorbed into a redefinition of α.

major comments (3)
  1. [Sections IV–VI, Eqs. (25)–(26), (39)–(44), (72)–(74)] Sec. IV–VI (Eqs. (25)–(26), (39)–(44), (72)–(74)): the central claim rests on taking the static free bumblebee Green function G(k) (unit residue of the pole denominator A(k)) as the potential felt by a nonrelativistic electron in the first-order Born formula. The Einstein-frame matter sector (8) is stated to contain nonlinear bumblebee–matter couplings, yet no electron–bumblebee vertex, charge/current, or residue of the physical e–e amplitude is derived, and the ordinary Coulomb photon is never separated from the bumblebee mode. Without that derivation, the overall factor 1/(1+ξb²/2), the P₂ modulation, the cross sections, and the |ξb²| bounds do not follow from the action.
  2. [Sections V and VII] Sec. V and VII: the manuscript treats the bumblebee-mediated potential both as “scattering induced by the bumblebee field” and as a uniform renormalization of the Coulomb strength used in Rutherford scattering and hydrogen spectroscopy. These are not equivalent. If the interaction is an additional long-range force, hydrogen bounds on α do not apply directly; if it is a modification of electromagnetism, that must be shown from the matter coupling to g_μν / h_μν. The present text leaves this identification ambiguous and load-bearing for the atomic constraints.
  3. [Section VII.A–B] Sec. VII.A–B: the isotropic bounds |ξb²| ≲ 8.1×10⁻¹¹ (timelike) and ≲ 2.4×10⁻¹⁰ (spacelike) are obtained by equating a fractional shift in Coulomb strength to an external α uncertainty ε_α ≃ 8.1×10⁻¹¹. As the paper itself notes, a pure isotropic rescaling can be absorbed into the definition of α; the quoted numbers are therefore only indicative and require an explicit, non-redundant constant set and a full hydrogen uncertainty budget before they can be presented as constraints on the model.
minor comments (5)
  1. [Abstract, Introduction] Abstract and several body paragraphs contain missing spaces around en-dashes (e.g., “investigatenon–metricityeffects”, “metric–affinebumblebee”).
  2. [Section III, Figure 1] Sec. III refers to “diagrams displayed in Fig. 1” for two-point vertices, but Fig. 1 is the timelike potential plot; figure numbering/captions need alignment.
  3. [Sections III.B–IV.B] Notation for the Lorentz-violating parameter switches among ξb², a≡ξb², and |b|² without a single consistent convention in the spacelike sections.
  4. [Figures 1–4] Figs. 1–4 would benefit from axis labels with units (or explicit natural units) and a clearer statement of which curves correspond to which ξb² values in the legends.
  5. [Section III] Eq. (11) is referenced as “Eq. (11)” for the Einstein-frame Lagrangian while the displayed equation numbering in the text is slightly out of step; renumber for consistency.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: propagator poles, static potentials, Born cross sections and atomic bounds are derived forward from the metric-affine action without reducing to fitted inputs or load-bearing self-citations.

full rationale

The derivation chain is self-contained. The metric-affine bumblebee action (1) is varied, the connection is integrated out to the Einstein-frame form (8), the fluctuation Lagrangian (11)–(13) and momentum-space propagator (14)–(18) are obtained by direct inversion, and the pole condition A(k)=0 supplies the dispersion relations (21) and (24). Static Green kernels follow by setting ω=0 and Fourier-transforming, producing the isotropic Coulomb potential (26) and the anisotropic potential (35)–(38) with explicit P₂ term. These V(r) are inserted into the first-order Born formula (40) and (73) to obtain Rutherford and orientation-dependent amplitudes and cross sections; no parameter is fitted to scattering data and then re-used as a prediction. Atomic bounds translate the same potentials into fractional energy shifts and compare them with external spectroscopic tolerances ε_H and ε_aniso; the paper itself notes that isotropic rescalings can be absorbed into α and therefore require an independent determination of the coupling. Self-citations supply background on related bumblebee solutions or thermodynamics and are not invoked as uniqueness theorems or as the sole justification for any load-bearing step. Consequently no step reduces by construction to its own input.

Assumptions & free parameters 3 free parameters · 7 assumptions · 1 invented entities

The central claim rests on the metric-affine bumblebee action and its Einstein-frame reduction (prior literature), the weak-field linear-in-ξ truncation, the standard quartic bumblebee potential, and the modeling step that equates the bumblebee static Green function with the electron interparticle potential used in Born scattering. Free parameters are the LV combination ξb² and auxiliary regulators (Yukawa α, angular cutoffs). No new particle species is invented; the bumblebee vector is inherited. Atomic bounds further assume that external α/ϱ determinations and published anisotropy sensitivities can be mapped linearly onto fractional energy shifts.

free parameters (3)
  • ξb² = bounded, not fitted; indicative |ξb²|≲8.1e-11 (timelike), ≲2.4e-10 (spacelike isotropic), ≲2.5e-15 to 2.5e-18 (quadrupol
    Dimensionless Lorentz-violating combination controlling all corrections to dispersion, potential, cross sections, and bounds; treated perturbatively with |ξb²|≪1 and constrained a posteriori rather than predicted.
  • λ (bumblebee potential coupling) = small positive; not numerically fixed
    Sets M²=λb²(±1+ξb²/4) and Λ=λ(1±2ξb²); enters the full propagator but drops out of the static massless Green kernels used for the long-range potentials.
  • α (Yukawa IR regulator) and θ_min / γ_min / y = α→0⁺; y, θ_min left free (e.g. y=0.12 in plots)
    Infrared cutoffs introduced by hand to regulate Coulomb divergences in amplitudes and total/transport cross sections; physical results depend on the chosen cutoff.
assumptions (7)
  • domain assumption Metric-affine bumblebee action with non-minimal ξB^α B^β R_αβ(Γ) coupling and independent connection (Eq. 1).
    Taken from Delhom et al.; defines the theory whose non-metricity effects are studied.
  • domain assumption Connection is auxiliary and can be integrated out to an Einstein-frame metric h_μν with disformal relation (Eq. 7).
    Sec. II; standard metric-affine reduction used throughout.
  • domain assumption Weak-field Minkowski limit with only O(ξ) terms retained; O(ξ²) discarded.
    Sec. III; controls all dispersion and potential expansions.
  • domain assumption Standard quartic potential V=λ/4(B²∓b²)² inducing VEV b_μ with spontaneous Lorentz breaking.
    Eq. (10); conventional bumblebee choice.
  • ad hoc to paper Static interparticle potential is the Fourier transform of the bumblebee propagator denominator (unit-coupled Green function) and is the potential felt by nonrelativistic electrons in Born scattering.
    Secs. IV–VI; load-bearing modeling step not derived from an explicit electron–bumblebee vertex in LM.
  • domain assumption First-order Born approximation (plus optional Mott/eikonal factors) adequately describes the scattering.
    Sec. V–VI; standard scattering theory assumption.
  • domain assumption Hydrogenic fractional shifts map linearly as δν/ν≃-ξb² (timelike) or (1/3)ξb² / (2/5)|ξb²| (spacelike pieces), comparable to external α precision or published ε_aniso.
    Sec. VII; used for indicative bounds only.
invented entities (1)
  • None beyond the pre-existing bumblebee vector field and its metric-affine non-metricity background independent evidence
    purpose: The paper applies an established LV vector model rather than introducing a new particle, force, or dimension.
    Bumblebee field and metric-affine realization are cited from prior work; no new mediator is postulated for the scattering calculation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Non-metricity effects on electron scattering in bumblebee gravity." pith.science (2026). https://pith.science/paper/ZMD5DDMB

@misc{pith2026260315959,
  author       = {Pith},
  title        = {Pith review of: Non-metricity effects on electron scattering in bumblebee gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZMD5DDMB}},
  note         = {Machine review of arXiv:2603.15959}
}
abstract

We investigate non-metricity effects on electron scattering in metric-affine bumblebee gravity, where spontaneous Lorentz symmetry breaking is induced by a vector field acquiring a nonzero vacuum expectation value. Treating the affine connection as an independent variable and integrating it out leads to an effective description in which non-metricity modifies the dispersion relation of the bumblebee modes. From the full momentum-space propagator, we determine the pole structure that governs the interaction and construct the corresponding static Green function and interparticle potential. For a purely timelike background, the dispersion relation remains isotropic and produces a Coulomb potential with a uniformly rescaled effective coupling; consequently, the scattering amplitude preserves the Rutherford angular dependence, with the Lorentz-violating parameter entering only as an overall multiplicative factor. In contrast, a spacelike background induces anisotropy in the dispersion relation, leading to an orientation-dependent potential characterized by a quadrupolar modulation. This anisotropic structure propagates to the differential and integrated cross sections, introducing directional dependence while preserving the long-range character of the interaction. Finally, we consider phenomenological constraints from atomic physics. Hydrogen spectroscopy constrains the isotropic sector associated with the timelike configuration, whereas searches for anisotropies provide stronger limits on the quadrupolar contribution governed by $\xi b^{2}$.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

60 extracted references

  1. [1]

    Differential cross section in the relativistic regime (Mott-type correction) 17

  2. [2]

    Eikonal formulation (high energy and small-angle scattering) 18

  3. [3]

    Scattering induced by the bumblebee field: spacelike configuration19 A

    Transport (momentum-transfer) cross section 18 VI. Scattering induced by the bumblebee field: spacelike configuration19 A. Electron scattering 19 VII. Bounds from atomic physics21 A. Timelike configuration ofb µ 21

  4. [4]

    Spacelike configuration ofb µ 22

    Hydrogen atom data 21 B. Spacelike configuration ofb µ 22

  5. [5]

    Isotropic piece andϱ–matching 23

  6. [6]

    Conclusion 25 IX

    Quadrupolar piece and anisotropy searches 24 VIII. Conclusion 25 IX. Acknowledgments26 X. Data Availability Statement26 References 26 2 I. INTRODUCTION Over the past decades, considerable effort has been devoted to investigating possible viola- tions of Lorentz symmetry. Early indications emerged within string–based constructions, where extended objects s...

    2000

  7. [7]

    A convenient way to incorporate this correction is to multiply the Rutherford–like result by the standard Mott factor

    Differential cross section in the relativistic regime (Mott-type correction) For relativistic electrons scattered by a static central potential, spin effects introduce a charac- teristic suppression at large angles. A convenient way to incorporate this correction is to multiply the Rutherford–like result by the standard Mott factor. Keeping the Born norma...

  8. [8]

    Eikonal formulation (high energy and small-angle scattering) An alternative treatment particularly suited to long–range interactions is the eikonal approxi- mation. Introducing the screened potential used in the regularization procedure, Vα(r) = geff r e−αr, α >0,(62) the eikonal phase at impact parameterbreads χ(b) =− 1 ℏv ˆ +∞ −∞ Vα √ b2 +z 2 dz=− 2geff...

Show all 60 references
  1. [9]

    Transport (momentum-transfer) cross section For long–range interactions the integrated cross section is dominated by the forward peak and depends strongly on the angular cutoff. A complementary quantity that is often closer to measurable momentum degradation is the transport, ...

  2. [10]

    Hydrogen atom data In the timelike configuration discussed above, the bumblebee background leaves the interaction Coulombic and modifies only its overall strength. In our notation, V(r) = 1 4πr 1 1 + ξb2 2 ≡ geff r , g eff ≡ 1 4π 1 + ξb2 2 ,(87) so that, for|ξb 2| ≪1, δg g ≡ g...

  3. [11]

    Isotropic piece andϱ–matching The first term in Eq. (98) is equivalent to an effective coupling ϱeff =ϱ 1 + ξb2 6 , δϱ ϱ ≃ ξb2 6 .(99) Therefore, any hydrogen observable with leading scalingO ∝ϱ p acquires δO O ≃p ξb2 6 ,(100) and in particular, for gross–structure transition ...

  4. [12]

    Quadrupolar piece and anisotropy searches The second term in Eq. (98) produces anm–dependent shift at first order in perturbation theory, δE(quad) nℓm =− ϱ ξb2 3 D1 r E nℓ D P2(cos ˆα) E ℓm .(104) For hydrogenic eigenstates|nℓm⟩, one may use the standard expectation values D1 ...

    2025

  5. [13]

    Phenomenological Gravitational Constraints on Strings and Higher Dimensional Theories,

    V. A. Kostelecky and S. Samuel, “Phenomenological Gravitational Constraints on Strings and Higher Dimensional Theories,”Phys. Rev. Lett., vol. 63, p. 224, 1989

    1989

  6. [14]

    Gravitational Phenomenology in Higher Dimensional Theories and Strings,

    V. A. Kostelecky and S. Samuel, “Gravitational Phenomenology in Higher Dimensional Theories and Strings,”Phys. Rev. D, vol. 40, pp. 1886–1903, 1989

    1903

  7. [15]

    CPT and strings,

    V. A. Kostelecky and R. Potting, “CPT and strings,”Nucl. Phys. B, vol. 359, pp. 545–570, 1991

    1991

  8. [16]

    CPT, strings, and meson factories,

    V. A. Kostelecky and R. Potting, “CPT, strings, and meson factories,”Phys. Rev. D, vol. 51, pp. 3923– 3935, 1995

    1995

  9. [17]

    Dirac-Born-Infeld action from spontaneous breakdown of Lorentz symmetry in brane- world scenarios,

    F. Gliozzi, “Dirac-Born-Infeld action from spontaneous breakdown of Lorentz symmetry in brane- world scenarios,”Phys. Rev. D, vol. 84, p. 027702, 2011

    2011

  10. [18]

    Nonstandard optics from quantum space-time,

    R. Gambini and J. Pullin, “Nonstandard optics from quantum space-time,”Phys. Rev. D, vol. 59, p. 124021, 1999

    1999

  11. [19]

    Lorentz violations in multifractal spacetimes,

    G. Calcagni, “Lorentz violations in multifractal spacetimes,”Eur. Phys. J. C, vol. 77, no. 5, p. 291, 2017. 26

    2017

  12. [20]

    On loop quantum gravity phenomenology and the issue of Lorentz invariance,

    M. Bojowald, H. A. Morales-Tecotl, and H. Sahlmann, “On loop quantum gravity phenomenology and the issue of Lorentz invariance,”Phys. Rev. D, vol. 71, p. 084012, 2005

    2005

  13. [21]

    Quantum gravity and Lorentz invariance deformation in the standard model,

    J. Alfaro, “Quantum gravity and Lorentz invariance deformation in the standard model,”Phys. Rev. Lett., vol. 94, p. 221302, 2005

    2005

  14. [22]

    A Phenomenological description of quantum gravity induced space-time noise,

    G. Amelino-Camelia, “A Phenomenological description of quantum gravity induced space-time noise,” Nature, vol. 410, pp. 1065–1067, 2001

    2001

  15. [23]

    CPT violation and the standard model,

    D. Colladay and V. A. Kostelecky, “CPT violation and the standard model,”Phys. Rev. D, vol. 55, pp. 6760–6774, 1997

    1997

  16. [24]

    Lorentz violating extension of the standard model,

    D. Colladay and V. A. Kostelecky, “Lorentz violating extension of the standard model,”Phys. Rev. D, vol. 58, p. 116002, 1998

    1998

  17. [25]

    Gravity, Lorentz violation, and the standard model,

    V. A. Kostelecky, “Gravity, Lorentz violation, and the standard model,”Phys. Rev. D, vol. 69, p. 105009, 2004

    2004

  18. [26]

    Gravity with a dynamical preferred frame,

    T. Jacobson and D. Mattingly, “Gravity with a dynamical preferred frame,”Phys. Rev. D, vol. 64, p. 024028, 2001

    2001

  19. [27]

    Chern-Simons modification of general relativity,

    R. Jackiw and S. Y. Pi, “Chern-Simons modification of general relativity,”Phys. Rev. D, vol. 68, p. 104012, 2003

    2003

  20. [28]

    Generalized bumblebee models and Lorentz-violating electrodynamics,

    M. D. Seifert, “Generalized bumblebee models and Lorentz-violating electrodynamics,”Phys. Rev. D, vol. 81, p. 065010, 2010

    2010

  21. [29]

    Exact Schwarzschild-like solution in a bumblebee gravity model,

    R. Casana, A. Cavalcante, F. P. Poulis, and E. B. Santos, “Exact Schwarzschild-like solution in a bumblebee gravity model,”Phys. Rev. D, vol. 97, no. 10, p. 104001, 2018

    2018

  22. [30]

    Influence of a Kalb-Ramond black hole on neutrino behavior,

    Y. Shi and A. A. Ara´ ujo Filho, “Influence of a Kalb-Ramond black hole on neutrino behavior,”JHEP, vol. 08, p. 028, 2025

    2025

  23. [31]

    Effects of bumblebee gravity on neutrino motion,

    Y. Shi and A. A. Ara´ ujo Filho, “Effects of bumblebee gravity on neutrino motion,”JCAP, vol. 11, p. 045, 2025

    2025

  24. [32]

    Exact traversable wormhole solution in bumblebee gravity,

    A. ¨Ovg¨ un, K. Jusufi, and ˙I. Sakallı, “Exact traversable wormhole solution in bumblebee gravity,” Phys. Rev. D, vol. 99, no. 2, p. 024042, 2019

    2019

  25. [33]

    Modified particle dynamics and thermodynamics in a traversable wormhole in bumblebee gravity,

    A. A. Ara´ ujo Filho, J. A. A. S. Reis, and A.¨Ovg¨ un, “Modified particle dynamics and thermodynamics in a traversable wormhole in bumblebee gravity,”Eur. Phys. J. C, vol. 85, no. 1, p. 83, 2025

    2025

  26. [34]

    Gravitational waves effects in a Lorentz–violating scenario,

    K. M. Amarilo, M. B. F. Filho, A. A. A. Filho, and J. A. A. S. Reis, “Gravitational waves effects in a Lorentz–violating scenario,”Phys. Lett. B, vol. 855, p. 138785, 2024

    2024

  27. [35]

    Black holes with a cosmological constant in bumblebee gravity,

    R. V. Maluf and J. C. S. Neves, “Black holes with a cosmological constant in bumblebee gravity,” Phys. Rev. D, vol. 103, no. 4, p. 044002, 2021

    2021

  28. [36]

    Einstein-Hilbert graviton modes modified by the Lorentz-violating bumblebee Field,

    R. V. Maluf, C. A. S. Almeida, R. Casana, and M. M. Ferreira, Jr., “Einstein-Hilbert graviton modes modified by the Lorentz-violating bumblebee Field,”Phys. Rev. D, vol. 90, no. 2, p. 025007, 2014

    2014

  29. [37]

    Constraints on Nonmetricity from Bounds on Lorentz 27 Violation,

    J. Foster, V. A. Kosteleck´ y, and R. Xu, “Constraints on Nonmetricity from Bounds on Lorentz 27 Violation,”Phys. Rev. D, vol. 95, no. 8, p. 084033, 2017

    2017

  30. [38]

    Riemann-Finsler geometry and Lorentz-violating kinematics,

    A. Kostelecky, “Riemann-Finsler geometry and Lorentz-violating kinematics,”Phys. Lett. B, vol. 701, pp. 137–143, 2011

    2011

  31. [39]

    Metric-affine bumblebee gravity: classical aspects,

    A. Delhom, J. R. Nascimento, G. J. Olmo, A. Y. Petrov, and P. J. Porf´ ırio, “Metric-affine bumblebee gravity: classical aspects,”Eur. Phys. J. C, vol. 81, no. 4, p. 287, 2021

    2021

  32. [40]

    Radiative corrections in metric-affine bumblebee model,

    A. Delhom, J. R. Nascimento, G. J. Olmo, A. Y. Petrov, and P. J. Porf´ ırio, “Radiative corrections in metric-affine bumblebee model,”Phys. Lett. B, vol. 826, p. 136932, 2022

    2022

  33. [41]

    Born–Infeld inspired modi- fications of gravity,

    J. Beltran Jimenez, L. Heisenberg, G. J. Olmo, and D. Rubiera-Garcia, “Born–Infeld inspired modi- fications of gravity,”Phys. Rept., vol. 727, pp. 1–129, 2018

    2018

  34. [42]

    Mapping Ricci-based theories of gravity into general relativity,

    V. I. Afonso, G. J. Olmo, and D. Rubiera-Garcia, “Mapping Ricci-based theories of gravity into general relativity,”Phys. Rev. D, vol. 97, no. 2, p. 021503, 2018

    2018

  35. [43]

    Mapping nonlinear gravity into General Relativity with nonlinear electrodynamics,

    V. I. Afonso, G. J. Olmo, E. Orazi, and D. Rubiera-Garcia, “Mapping nonlinear gravity into General Relativity with nonlinear electrodynamics,”Eur. Phys. J. C, vol. 78, no. 10, p. 866, 2018

    2018

  36. [44]

    Ricci-Based Gravity theories and their impact on Maxwell and nonlinear electromagnetic models,

    A. Delhom, G. J. Olmo, and E. Orazi, “Ricci-Based Gravity theories and their impact on Maxwell and nonlinear electromagnetic models,”JHEP, vol. 11, p. 149, 2019

    2019

  37. [45]

    Ghosts in metric-affine higher order curvature gravity,

    J. Beltr´ an Jim´ enez and A. Delhom, “Ghosts in metric-affine higher order curvature gravity,”Eur. Phys. J. C, vol. 79, no. 8, p. 656, 2019

    2019

  38. [46]

    Quasinormal modes, and different aspects of Hawking radiation within the metric-affine bumblebee gravity framework,

    S. K. Jha and A. Rahaman, “Quasinormal modes, and different aspects of Hawking radiation within the metric-affine bumblebee gravity framework,”Nucl. Phys. B, vol. 1002, p. 116536, 2024

    2024

  39. [47]

    Probing Schwarzschild-like black holes in metric-affine bumblebee gravity with accretion disk, deflection angle, greybody bounds, and neutrino propagation,

    G. Lambiase, L. Mastrototaro, R. C. Pantig, and A. Ovgun, “Probing Schwarzschild-like black holes in metric-affine bumblebee gravity with accretion disk, deflection angle, greybody bounds, and neutrino propagation,”JCAP, vol. 12, p. 026, 2023

    2023

  40. [48]

    The role of non-metricity on neutrino behavior in bumblebee gravity,

    Y. Shi and A. A. Ara´ ujo Filho, “The role of non-metricity on neutrino behavior in bumblebee gravity,” 5 2025

    2025

  41. [49]

    Scattering effects of bumblebee gravity in metric-affine formalism,

    N. Heidari, C. F. B. Macedo, A. A. A. Filho, and H. Hassanabadi, “Scattering effects of bumblebee gravity in metric-affine formalism,”Eur. Phys. J. C, vol. 84, no. 11, p. 1221, 2024

    2024

  42. [50]

    Gravitational lensing by a Lorentz-violating black hole,

    A. A. A. Filho, J. R. Nascimento, A. Y. Petrov, and P. J. Porf´ ırio, “Gravitational lensing by a Lorentz-violating black hole,”Eur. Phys. J. Plus, vol. 140, no. 11, p. 1117, 2025

    2025

  43. [51]

    Lensing Fingerprints of Scalar Hair and Broken Symmetries via Three Semi-Analytical Methods,

    A. ¨Ovg¨ un and R. C. Pantig, “Lensing Fingerprints of Scalar Hair and Broken Symmetries via Three Semi-Analytical Methods,” 7 2025

    2025

  44. [52]

    Scalar-metric-affine theories: Can we get ghost-free theories from symme- try?,

    K. Aoki and K. Shimada, “Scalar-metric-affine theories: Can we get ghost-free theories from symme- try?,”Phys. Rev. D, vol. 100, no. 4, p. 044037, 2019

    2019

  45. [53]

    Constraints and Stability in Vector Theories with Spontaneous Lorentz Violation,

    R. Bluhm, N. L. Gagne, R. Potting, and A. Vrublevskis, “Constraints and Stability in Vector Theories with Spontaneous Lorentz Violation,”Phys. Rev. D, vol. 77, p. 125007, 2008. [Erratum: Phys.Rev.D 79, 029902 (2009)]. 28

    2008

  46. [54]

    Spontaneous Lorentz violation and nonpolynomial interactions,

    B. Altschul and V. A. Kostelecky, “Spontaneous Lorentz violation and nonpolynomial interactions,” Phys. Lett. B, vol. 628, pp. 106–112, 2005

    2005

  47. [55]

    Elastic scattering of electron by a Yukawa potential in non-commutative spacetime,

    A. Touati, “Elastic scattering of electron by a Yukawa potential in non-commutative spacetime,”Phys. Lett. B, vol. 867, p. 139598, 2025

    2025

  48. [56]

    Thermodynamic properties of neutral dirac particles in the presence of an electro- magnetic field,

    R. Oliveiraet al., “Thermodynamic properties of neutral dirac particles in the presence of an electro- magnetic field,”The European Physical Journal Plus, vol. 135, no. 1, pp. 1–10, 2020

    2020

  49. [57]

    Modified particle dynamics and thermodynamics in a traversable wormhole in bumblebee gravity,

    A. A Ara´ ujo Filho, J. A. A. S. Reis, and A.¨Ovg¨ un, “Modified particle dynamics and thermodynamics in a traversable wormhole in bumblebee gravity,”The European Physical Journal C, vol. 85, no. 1, p. 83, 2025

    2025

  50. [58]

    The relativistic aharonov–bohm– coulomb system with position-dependent mass,

    R. Oliveira, A. A. Ara´ ujo Filho, R. V. Maluf, and C. Almeida, “The relativistic aharonov–bohm– coulomb system with position-dependent mass,”Journal of Physics A: Mathematical and Theoretical, vol. 53, no. 4, p. 045304, 2020

    2020

  51. [59]

    How does geometry affect quantum gases?,

    A. A. Ara´ ujo Filho and J. A. A. S. Reis, “How does geometry affect quantum gases?,”International Journal of Modern Physics A, vol. 37, no. 11n12, p. 2250071, 2022

    2022

  52. [60]

    Particles in loop quantum gravity formalism: a thermodynamical description,

    A. A. Ara´ ujo Filho, “Particles in loop quantum gravity formalism: a thermodynamical description,” Annalen der Physik, vol. 534, no. 12, p. 2200383, 2022. 29

    2022

Pith tools

Reviewed July 14, 2026 · model on record in the stance chip above.