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arxiv: 2606.02329 · v1 · pith:DYSQN2CHnew · submitted 2026-06-01 · 🌀 gr-qc · hep-th

Equivalence Principle violation in metric-affine gravity and finite-temperature effects

Emmanuele Battista , Roberto Campagnola , Salvatore Capozziello , Giuseppe Fiorillo This is my paper

Pith reviewed 2026-06-28 13:18 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords equivalence principlemetric-affine gravitynon-metricityfinite temperatureuniversal free fallFermi-Walker derivativegravitational massinertial mass
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The pith

Non-metricity in metric-affine gravity produces the same gravitational-to-inertial mass ratio shift as finite-temperature effects.

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

The paper establishes that thermal corrections to particle dynamics produce a shift between gravitational and inertial mass, breaking the universality of free fall, and that these corrections admit a purely geometric description inside Riemannian geometry. The same mass-ratio shift and departure from universal free fall can be reproduced in metric-affine gravity once the non-metricity tensor is allowed to act on the Newtonian limit. A generalized Fermi-Walker derivative adapted to non-Riemannian geometry is introduced; it shows that no orthonormal tetrad can be transported along an observer worldline. This supplies a geometric signature that the modern statement of the equivalence principle fails to hold in general, even though a pointwise gauge-theoretic version remains possible.

Core claim

Thermal corrections to particle dynamics, originally obtained in a quantum-field-theory setting, can be re-derived inside a purely Riemannian framework and yield a shift in the gravitational-to-inertial mass ratio. The resulting violation of the universality of free fall admits an equivalent formulation in metric-affine gravity, where the non-metricity tensor modifies the Newtonian law in a closely parallel manner. A generalized Fermi-Walker derivative defined for non-Riemannian spacetimes further shows that orthonormal tetrads cannot be propagated along observer worldlines, furnishing a direct geometric indication that the equivalence principle in its modern formulation is not retained.

What carries the argument

The non-metricity tensor, which alters the Newtonian force law to reproduce the finite-temperature mass-ratio shift, together with the generalized Fermi-Walker derivative that prevents propagation of orthonormal tetrads along worldlines.

If this is right

  • Departures from universal free fall appear in both the finite-temperature and metric-affine descriptions.
  • No orthonormal tetrad can be carried along an observer worldline once non-metricity is present.
  • Metric-affine gravity still permits a pointwise gauge-theoretic realization of the Einstein equivalence principle but not its modern formulation.
  • Observational tests of the mass-ratio shift become relevant for both thermal and geometric sources.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Laboratory tests that vary temperature while monitoring free-fall accelerations could place independent limits on non-metricity parameters.
  • The same mass-ratio shift might appear in other modified-gravity models that introduce non-metricity or torsion.
  • Frame-transport experiments along closed paths could search for the predicted inability to maintain orthonormal tetrads.

Load-bearing premise

Thermal corrections derived in quantum field theory can be evaluated inside a purely Riemannian geometry and produce a shift in the gravitational-to-inertial mass ratio.

What would settle it

A laboratory measurement of whether the free-fall acceleration of test bodies changes with temperature in quantitative agreement with the predicted mass-ratio shift, or an astronomical bound on non-metricity parameters that would force the same shift.

read the original abstract

Possible violations of the equivalence principle are investigated within the framework of metric-affine gravity and their connection to finite-temperature effects are highlighted. Thermal corrections to particle dynamics, originally derived in a quantum-field-theory setting, can be evaluated in a purely Riemannian framework and lead to a shift in the gravitational-to-inertial mass ratio. We show that the ensuing departure from universality of free fall can be also formulated in metric-affine gravity, where the presence of the non-metricity tensor modifies the Newtonian law in a way that closely parallels the finite-temperature scenario. Furthermore, we introduce a generalized Fermi-Walker derivative adapted to non-Riemannian contexts, which naturally reveals that no orthonormal tetrad can be propagated along an observer worldline. Although metric-affine gravity admits a pointwise realization of the Einstein equivalence principle in its gauge-theoretic, elementary-matter form, the new operator offers a direct geometric signature that this principle, in its modern formulation, is not retained in general. Potential tests of the analyzed effects are also discussed.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper investigates possible violations of the equivalence principle in metric-affine gravity and their connection to finite-temperature effects. It claims that thermal corrections to particle dynamics from QFT can be recast in a purely Riemannian framework, producing a shift in the gravitational-to-inertial mass ratio that departs from universality of free fall. This effect is paralleled in metric-affine gravity via the non-metricity tensor modifying the Newtonian law. A generalized Fermi-Walker derivative adapted to non-Riemannian geometry is introduced, showing that no orthonormal tetrad can be propagated along an observer worldline. The work distinguishes a pointwise gauge-theoretic realization of the Einstein equivalence principle (admitted in metric-affine gravity) from its modern formulation (not retained in general), and discusses potential tests.

Significance. If the mapping from QFT thermal corrections to a Riemannian mass-ratio shift and its geometric parallel in non-metricity is rigorously justified, the result would link quantum thermal effects to classical geometric modifications of free fall, offering a concrete signature for equivalence-principle violation in metric-affine theories and suggesting new experimental probes.

major comments (2)
  1. [Abstract] The central claim that thermal corrections originally derived in QFT can be evaluated in a purely Riemannian framework to produce a concrete shift in the gravitational-to-inertial mass ratio (and thereby parallel the non-metricity modification) is load-bearing for the asserted equivalence between the two frameworks, yet no derivation or explicit effective force law is supplied to confirm that the result follows from the Riemannian geodesic equation alone without retaining quantum-field or non-Riemannian ingredients.
  2. [Abstract] The introduction of the generalized Fermi-Walker derivative and the conclusion that it provides a direct geometric signature that the modern formulation of the equivalence principle is not retained in general relies on the operator's definition and its action on tetrads; without the explicit construction or proof that no orthonormal tetrad can be propagated, the distinction between the gauge-theoretic pointwise EEP and the modern formulation cannot be verified.
minor comments (1)
  1. [Abstract] The abstract states that the non-metricity tensor 'modifies the Newtonian law in a way that closely parallels the finite-temperature scenario,' but the precise form of the modification and the parallel (e.g., identical functional dependence on the mass-ratio shift) is not shown.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying points where additional explicit derivations would improve clarity. We address each major comment below and will revise the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: [Abstract] The central claim that thermal corrections originally derived in QFT can be evaluated in a purely Riemannian framework to produce a concrete shift in the gravitational-to-inertial mass ratio (and thereby parallel the non-metricity modification) is load-bearing for the asserted equivalence between the two frameworks, yet no derivation or explicit effective force law is supplied to confirm that the result follows from the Riemannian geodesic equation alone without retaining quantum-field or non-Riemannian ingredients.

    Authors: We agree that the presentation would benefit from an explicit derivation. While the manuscript derives the mass-ratio shift by recasting the thermal corrections as an effective modification to the geodesic equation in a Riemannian setting, we will add a dedicated subsection with the step-by-step derivation of the effective force law (including the explicit form of the correction term) to confirm that the result follows solely from the Riemannian structure without quantum-field or non-Riemannian ingredients. revision: yes

  2. Referee: [Abstract] The introduction of the generalized Fermi-Walker derivative and the conclusion that it provides a direct geometric signature that the modern formulation of the equivalence principle is not retained in general relies on the operator's definition and its action on tetrads; without the explicit construction or proof that no orthonormal tetrad can be propagated, the distinction between the gauge-theoretic pointwise EEP and the modern formulation cannot be verified.

    Authors: We acknowledge that the explicit construction and proof are essential for verifiability. The manuscript defines the generalized Fermi-Walker derivative and states the result on tetrad propagation, but we will expand the relevant section to include the full operator definition, its action on an arbitrary tetrad, and the detailed proof that no orthonormal tetrad can be propagated along the observer worldline, thereby making the distinction between the two formulations of the EEP explicit. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rely on external QFT results and independent geometric reformulation

full rationale

The abstract states that thermal corrections 'originally derived in a quantum-field-theory setting, can be evaluated in a purely Riemannian framework' and that the resulting mass-ratio shift 'can be also formulated in metric-affine gravity'. No equations, derivation steps, or self-citations appear in the visible text. Because no load-bearing step is shown that reduces a prediction to its own fitted input or to a prior self-citation by construction, the derivation chain cannot be exhibited as circular. The mapping is presented as a reformulation whose validity rests on external benchmarks rather than internal redefinition.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no information on free parameters, axioms, or invented entities.

pith-pipeline@v0.9.1-grok · 5712 in / 1059 out tokens · 22111 ms · 2026-06-28T13:18:16.377922+00:00 · methodology

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Works this paper leans on

165 extracted references · 4 canonical work pages

  1. [1]

    The anomalous acceleration The existence of a nonzero non-metricity tensor (5) en- tails significant consequences for the spacetime structure, mainly because care must be taken when evaluating the covariant derivative of covariant or contravariant vectors (cf. Eq. (6)). In general, the main effects introduced byQ λµν are: (i) lengths and angles are typica...

  2. [2]

    The gauging procedure of the affine group The key idea characterizing metric-affine gravity fol- lows from the gauge-theoretic principle that the descrip- tion of physics should be independent of the choice of reference frames used to express the dynamical variables of the theory. The starting point then consists in requiring that phys- ical matter fields...

  3. [3]

    The equivalence principle In this section, we explain how the Einstein EP, in its gauge-theoretic formulation, is realized in MAG. The starting point is that, for every eventxPM, there exists a suitable anholonomic system where gab|x ‹“η ab,(23a) Γa b|x ‹“0.(23b) This is a purely pointwise gauge statement, following from the localGLp4,Rqfreedom of metric-...

  4. [4]

    This highlights a structural relation with the gauge principle introduced in Sec

    The role of the gauge principle From the analysis of the previous section, it is clear that in MAG the pointwise gauge version of the Einstein EPisretainedand thatitisimplementedmathematically via the minimal coupling principle of matter to gravity [58, 83]. This highlights a structural relation with the gauge principle introduced in Sec. IIC1 [73, 74, 76...

  5. [5]

    Quantum diagrammatic approach In their seminal papers [54, 55], Donoghue and collab- orators exploited finite-temperature QFT tools to com- pute the corrections to the electron self-energy occurring in a low-temperature environment, where T!m 0,(24) m0 being the renormalizedT“0electron mass. In this regime, the background temperature is mainly provided by...

  6. [6]

    fine structure

    Classical relativistic approach A complementary analysis was carried out by Gasperini [56], who investigated thermal effects on the gravitational acceleration of relativistic particles in the low-temperature limit (24), within a weak and static gravitational field. Unlike the previous investigation, which relies on diagrammatic techniques from finite- tem...

  7. [7]

    ˝ P ∥ µ α

    Riemannian spacetime In a Riemannian spacetime, let there be given a time- like curve, and introduce the projection operators ˝ P ∥ α µ “ ´9xα 9xµ ,(73a) ˝ P K α µ “δα µ `9xα 9xµ ,(73b) which allow any tensorial quantity to be decomposed into components parallel and orthogonal to the tangent vector 9xµ to the curve. Thus, the projection of the Riemannian ...

  8. [8]

    IIC1), which entails varying- magnitude vectors and gives rise to two different accel- erations, namely the proper and the anomalous one (cf

    Metric-affine spacetime As we set out before, the local violation of the Lorentz invariance in metric-affine spacetime is related to the presence of the non-metricity tensor (5) (or, equivalently, the one-formQ ab, see Sec. IIC1), which entails varying- magnitude vectors and gives rise to two different accel- erations, namely the proper and the anomalous ...

  9. [9]

    Romano and M

    A. Romano and M. Furnari,The Physical and Mathe- matical Foundations of the Theory of Relativity: A Crit- ical Analysis(Springer International Publishing, 2019)

    2019

  10. [10]

    A. G. Lebed, Mod. Phys. Lett. A35, 2030010 (2020), arXiv:2006.14073 [gr-qc]

    arXiv 2020

  11. [11]

    Mitchell and C

    T. Mitchell and C. M. Will, Phys. Rev. D75, 124025 (2007), arXiv:0704.2243 [gr-qc]

    Pith/arXiv arXiv 2007

  12. [12]

    C. M. Will, Phys. Rev. D111, 104034 (2025), arXiv:2503.03189 [gr-qc]

    arXiv 2025

  13. [13]

    C. M. Will, Living Rev. Rel.17, 4 (2014), arXiv:1403.7377 [gr-qc]

    Pith/arXiv arXiv 2014

  14. [14]

    Bertiet al., Class

    E. Bertiet al., Class. Quant. Grav.32, 243001 (2015), arXiv:1501.07274 [gr-qc]

    Pith/arXiv arXiv 2015

  15. [15]

    Pérezet al., Hyperfine Interactions233, 21 (2015)

    P. Pérezet al., Hyperfine Interactions233, 21 (2015)

    2015

  16. [16]

    Viswanathan, A

    V. Viswanathan, A. Fienga, O. Minazzoli, L. Bernus, J. Laskar, and M. Gastineau, Mon. Not. Roy. Astron. Soc.476, 1877 (2018), arXiv:1710.09167 [gr-qc]

    Pith/arXiv arXiv 2018

  17. [17]

    C. M. Will,Theory and Experiment in Gravitational Physics(Cambridge University Press, 2018)

    2018

  18. [18]

    Belenchiaet al., Phys

    A. Belenchiaet al., Phys. Rept.951, 1 (2022), arXiv:2108.01435 [quant-ph]

    arXiv 2022

  19. [19]

    T. A. Wagner, S. Schlamminger, J. H. Gundlach, and E. G. Adelberger, Class. Quant. Grav.29, 184002 (2012), arXiv:1207.2442 [gr-qc]

    Pith/arXiv arXiv 2012

  20. [20]

    C.Overstreet, P.Asenbaum, T.Kovachy, R.Notermans, J.M.Hogan, andM.A.Kasevich,Phys.Rev.Lett.120, 183604 (2018), arXiv:1711.09986 [physics.atom-ph]

    Pith/arXiv arXiv 2018

  21. [21]

    Asenbaum, C

    P. Asenbaum, C. Overstreet, M. Kim, J. Curti, and M. A. Kasevich, Phys. Rev. Lett.125, 191101 (2020), arXiv:2005.11624 [physics.atom-ph]

    arXiv 2020

  22. [22]

    G. M. Tino, L. Cacciapuoti, S. Capozziello, G. Lambi- ase, and F. Sorrentino, Prog. Part. Nucl. Phys.112, 103772 (2020), arXiv:2002.02907 [gr-qc]

    arXiv 2020

  23. [23]

    Touboulet al., Phys

    P. Touboulet al., Phys. Rev. Lett.119, 231101 (2017), arXiv:1712.01176 [astro-ph.IM]

    Pith/arXiv arXiv 2017

  24. [24]

    Touboulet al.(MICROSCOPE), Phys

    P. Touboulet al.(MICROSCOPE), Phys. Rev. Lett. 129, 121102 (2022), arXiv:2209.15487 [gr-qc]

    arXiv 2022

  25. [25]

    J. P. Pereira, J. M. Overduin, and A. J. Poyneer, Phys. Rev.Lett.117,071103(2016),arXiv:1607.06944[gr-qc]

    Pith/arXiv arXiv 2016

  26. [26]

    A. M. Nobiliet al., Class. Quant. Grav.29, 184011 (2012)

    2012

  27. [27]

    Gaaloulet al.(STE-QUEST), (2022), arXiv:2211.15412 [physics.space-ph]

    N. Gaaloulet al.(STE-QUEST), (2022), arXiv:2211.15412 [physics.space-ph]

    arXiv 2022

  28. [28]

    Cacciapuotiet al., J

    L. Cacciapuotiet al., J. Phys. Conf. Ser.2889, 012005 (2024), arXiv:2411.02912 [gr-qc]

    arXiv 2024

  29. [29]

    J. G. Williams, S. G. Turyshev, and D. H. Boggs, Int. J. Mod. Phys. D18, 1129 (2009), arXiv:gr-qc/0507083

    Pith/arXiv arXiv 2009

  30. [30]

    J. G. Williams, S. G. Turyshev, and D. Boggs, Class. Quant. Grav.29, 184004 (2012), arXiv:1203.2150 [gr- qc]

    Pith/arXiv arXiv 2012

  31. [31]

    Congedo and F

    G. Congedo and F. De Marchi, Phys. Rev. D93, 102003 (2016), arXiv:1602.05949 [gr-qc]

    Pith/arXiv arXiv 2016

  32. [32]

    March, O

    R. March, O. Bertolami, M. Muccino, and S. Dell’Agnello, Phys. Rev. D109, 124013 (2024), arXiv:2312.14618 [gr-qc]

    arXiv 2024

  33. [33]

    Kraiselburd, S

    L. Kraiselburd, S. J. Landau, M. Salgado, D. Sudarsky, and H. Vucetich, Phys. Rev. D99, 083516 (2019), arXiv:1904.05431 [gr-qc]

    Pith/arXiv arXiv 2019

  34. [34]

    Damour and J

    T. Damour and J. F. Donoghue, Class. Quant. Grav. 27, 202001 (2010), arXiv:1007.2790 [gr-qc]

    Pith/arXiv arXiv 2010

  35. [35]

    Armendariz-Picon and R

    C. Armendariz-Picon and R. Penco, Phys. Rev. D85, 044052 (2012), arXiv:1108.6028 [hep-th]

    Pith/arXiv arXiv 2012

  36. [36]

    Zhang, R

    X. Zhang, R. Niu, and W. Zhao, Phys. Rev. D100, 024038 (2019), arXiv:1906.10791 [gr-qc]. 17

    Pith/arXiv arXiv 2019

  37. [37]

    Damour and G

    T. Damour and G. Esposito-Farese, Phys. Rev. Lett. 70, 2220 (1993)

    1993

  38. [38]

    Kuntz and E

    A. Kuntz and E. Barausse, Phys. Rev. D109, 124001 (2024), arXiv:2403.07980 [gr-qc]

    arXiv 2024

  39. [39]

    K. Yagi, D. Blas, E. Barausse, and N. Yunes, Phys. Rev. D89, 084067 (2014), [Erratum: Phys.Rev.D 90, 069902 (2014), Erratum: Phys.Rev.D 90, 069901 (2014)], arXiv:1311.7144 [gr-qc]

    Pith/arXiv arXiv 2014

  40. [40]

    Skordis, Classical and Quantum Gravity26, 143001 (2009), arXiv:0903.3602 [astro-ph.CO]

    C. Skordis, Classical and Quantum Gravity26, 143001 (2009), arXiv:0903.3602 [astro-ph.CO]

    Pith/arXiv arXiv 2009

  41. [41]

    Famaey and S

    B. Famaey and S. McGaugh, Living Rev. Rel.15, 10 (2012), arXiv:1112.3960 [astro-ph.CO]

    Pith/arXiv arXiv 2012

  42. [42]

    Uzan, Rev

    J.-P. Uzan, Rev. Mod. Phys.75, 403 (2003), arXiv:hep- ph/0205340

    arXiv 2003

  43. [43]

    Uzan, Living Rev

    J.-P. Uzan, Living Rev. Rel.14, 2 (2011), arXiv:1009.5514 [astro-ph.CO]

    Pith/arXiv arXiv 2011

  44. [44]

    V. A. Dzuba, V. V. Flambaum, and A. J. Mansour, Phys. Rev. D110, 055022 (2024), arXiv:2402.09643 [hep-ph]

    arXiv 2024

  45. [45]

    Bileska, Class

    M. Bileska, Class. Quant. Grav.41, 183001 (2024)

    2024

  46. [46]

    A. V. Belikov and W. Hu, Phys. Rev. D87, 084042 (2013), arXiv:1212.0831 [gr-qc]

    Pith/arXiv arXiv 2013

  47. [47]

    Hiramatsu, W

    T. Hiramatsu, W. Hu, K. Koyama, and F. Schmidt, Phys. Rev. D87, 063525 (2013), arXiv:1209.3364 [hep- th]

    Pith/arXiv arXiv 2013

  48. [48]

    G. J. Olmo, Phys. Rev. Lett.98, 061101 (2007), arXiv:gr-qc/0612002

    Pith/arXiv arXiv 2007

  49. [49]

    N. E. Mavromatos, Lect. Notes Phys.1017, 3 (2023), arXiv:2205.07044 [hep-th]

    arXiv 2023

  50. [50]

    Lammerzahl, Gen

    C. Lammerzahl, Gen. Rel. Grav.28, 1043 (1996), arXiv:gr-qc/9605065

    Pith/arXiv arXiv 1996

  51. [51]

    Zych and Č

    M. Zych and Č. Brukner, Nature Phys.14, 1027 (2018), arXiv:1502.00971 [gr-qc]

    Pith/arXiv arXiv 2018

  52. [52]

    Seveso, V

    L. Seveso, V. Peri, and M. G. A. Paris, J. Phys. Conf. Ser.880, 012067 (2017), arXiv:1702.07526 [gr-qc]

    Pith/arXiv arXiv 2017

  53. [53]

    Cepollaro and F

    C. Cepollaro and F. Giacomini, Class. Quant. Grav.41, 185009 (2024), arXiv:2112.03303 [quant-ph]

    arXiv 2024

  54. [54]

    N. E. J. Bjerrum-Bohr, J. F. Donoghue, B. R. Hol- stein, L. Planté, and P. Vanhove, Phys. Rev. Lett.114, 061301 (2015), arXiv:1410.7590 [hep-th]

    Pith/arXiv arXiv 2015

  55. [55]

    N. E. J. Bjerrum-Bohr, J. F. Donoghue, B. R. Hol- stein, L. Plante, and P. Vanhove, JHEP11, 117 (2016), arXiv:1609.07477 [hep-th]

    Pith/arXiv arXiv 2016

  56. [56]

    Bai and Y

    D. Bai and Y. Huang, Phys. Rev. D95, 064045 (2017), arXiv:1612.07629 [hep-th]

    Pith/arXiv arXiv 2017

  57. [57]

    Chi, Phys

    H.-H. Chi, Phys. Rev. D99, 126008 (2019), arXiv:1903.07944 [hep-th]

    Pith/arXiv arXiv 2019

  58. [58]

    A. K. Das,Finite Temperature Field Theory(World Sci- entific, New York, 1997)

    1997

  59. [59]

    J. I. Kapusta and C. Gale,Finite-Temperature Field Theory : Principles and Applications, 2nd edition (Cambridge University Press, 2007)

    2007

  60. [60]

    F. C. Khanna, A. P. C. Malbouisson, J. M. C. Malbouis- son, and A. R. Santana,Thermal quantum field theory - Algebraic aspects and applications(2009)

    2009

  61. [61]

    M. G. Mustafa, Eur. Phys. J. ST232, 1369 (2023), arXiv:2207.00534 [hep-ph]

    arXiv 2023

  62. [62]

    J. F. Donoghue, B. R. Holstein, and R. W. Robinett, Phys. Rev. D30, 2561 (1984)

    1984

  63. [63]

    J. F. Donoghue, B. R. Holstein, and R. W. Robinett, Gen. Rel. Grav.17, 207 (1985)

    1985

  64. [64]

    Gasperini, Phys

    M. Gasperini, Phys. Rev. D36, 617 (1987)

    1987

  65. [65]

    Blasone, S

    M. Blasone, S. Capozziello, G. Lambiase, and L. Petruzziello, Int. J. Geom. Meth. Mod. Phys.19, 2250055 (2022), arXiv:2112.08480 [gr-qc]

    arXiv 2022

  66. [66]

    Von Der Heyde, Lettere al Nuovo Cimento (1971- 1985)14, 250 (1975)

    P. Von Der Heyde, Lettere al Nuovo Cimento (1971- 1985)14, 250 (1975)

    1971

  67. [67]

    F. W. Hehl, P. Von Der Heyde, G. D. Kerlick, and J. M. Nester, Rev. Mod. Phys.48, 393 (1976)

    1976

  68. [68]

    Y. N. Obukhov and F. W. Hehl (2023) arXiv:2311.03160 [gr-qc]

    arXiv 2023

  69. [69]

    Y. N. Obukhov and F. W. Hehl, (2024), 10.1002/andp.202400217, arXiv:2409.19411 [gr-qc]

    work page doi:10.1002/andp.202400217 2024

  70. [70]

    J. A. Schouten,Ricci-Calculus(Springer, Berlin, 1954)

    1954

  71. [71]

    Nakahara,Geometry, topology and physics(2003)

    M. Nakahara,Geometry, topology and physics(2003)

    2003

  72. [72]

    Bahamondeet al., Rept

    S. Bahamondeet al., Rept. Prog. Phys.86, 026901 (2023), arXiv:2106.13793 [gr-qc]

    arXiv 2023

  73. [73]

    Capozziello, V

    S. Capozziello, V. De Falco, and C. Ferrara, Eur. Phys. J. C82, 865 (2022), arXiv:2208.03011 [gr-qc]

    arXiv 2022

  74. [74]

    Annala and S

    J. Annala and S. Rasanen, JCAP04, 014 (2023), [Er- ratum: JCAP 08, E02 (2023), Erratum: JCAP 05, E01 (2025)], arXiv:2212.09820 [gr-qc]

    arXiv 2023

  75. [75]

    Capozziello, S

    S. Capozziello, S. Cesare, and C. Ferrara, Eur. Phys. J. C85, 932 (2025), arXiv:2503.08167 [gr-qc]

    arXiv 2025

  76. [76]

    Battista, S

    E. Battista, S. Capozziello, and S. Pastore, Eur. Phys. J. C86, 298 (2026), arXiv:2603.00596 [gr-qc]

    arXiv 2026

  77. [77]

    Iosifidis, C

    D. Iosifidis, C. G. Tsagas, and A. C. Petkou, Phys. Rev. D98, 104037 (2018), arXiv:1809.04992 [gr-qc]

    Pith/arXiv arXiv 2018

  78. [78]

    Agashe, Phys

    A. Agashe, Phys. Scripta98, 105210 (2023), arXiv:2303.08960 [gr-qc]

    arXiv 2023

  79. [79]

    Agashe, Int

    A. Agashe, Int. J. Geom. Meth. Mod. Phys.21, 2450120 (2024), arXiv:2312.06418 [gr-qc]

    arXiv 2024

  80. [80]

    Capozziello and C

    S. Capozziello and C. Ferrara, Int. J. Geom. Meth. Mod. Phys.21, 2440014 (2024), arXiv:2401.09737 [gr-qc]

    arXiv 2024

Showing first 80 references.