On black holes in new general relativity
Pith reviewed 2026-05-18 20:16 UTC · model grok-4.3
The pith
In New General Relativity, torsion scalars diverge at local black hole horizons for every viable parameter choice.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Assuming such horizons exist, we demonstrate that all physically viable NGR models—including the Teleparallel Equivalent of General Relativity (TEGR) and the one-parameter Hayashi and Shirafuji model (1P-H&S)—inevitably exhibit divergences in torsion scalars at the local horizon. This singular behavior obstructs the interpretation of these models and their associated teleparallel geometries as black hole configurations.
What carries the argument
Torsion scalars of the teleparallel connection, evaluated at horizons located by the expansion of null congruences.
If this is right
- The Teleparallel Equivalent of General Relativity cannot host regular black-hole horizons.
- The one-parameter Hayashi-Shirafuji model exhibits the same divergence in torsion scalars.
- Every NGR model consistent with experimental bounds is obstructed from describing black holes.
- Standard black-hole solutions of general relativity do not extend to these teleparallel geometries without singularities.
Where Pith is reading between the lines
- Different notions of horizon may be required in teleparallel gravity that do not rely on metric null congruences.
- Non-minimal coupling of matter to the geometry might remove the divergence.
- Similar torsion singularities could appear in other modified-gravity theories that replace curvature with torsion.
- Numerical simulations of gravitational collapse in NGR would be a direct test of whether the divergence appears dynamically.
Load-bearing premise
Local horizons can be identified and analyzed using null congruence expansions in the same way as in metric theories, while matter couples minimally to the metric so that test particles follow geodesics.
What would settle it
An explicit construction of a black-hole solution in any viable NGR model in which all torsion scalars remain finite at the horizon would disprove the claim.
read the original abstract
New General Relativity (NGR) is a class of teleparallel theories defined by three free parameters, effectively reduced to two after appropriate normalization, which are subject to experimental constraints. In this framework, matter couples minimally to the metric, ensuring that test particles follow geodesics and that null congruence expansions can be employed to detect local horizons. Assuming such horizons exist, we demonstrate that all physically viable NGR models--including the Teleparallel Equivalent of General Relativity (TEGR) and the one-parameter Hayashi and Shirafuji model (1P-H&S)--inevitably exhibit divergences in torsion scalars at the local horizon. This singular behavior obstructs the interpretation of these models and their associated teleparallel geometries as black hole configurations.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper investigates black hole solutions in New General Relativity (NGR), a teleparallel gravity theory with two free parameters after normalization. Assuming local horizons exist and can be identified via metric null congruence expansions (since matter couples minimally to the metric), it claims that torsion scalars diverge at these horizons for all physically viable NGR models, including TEGR and the one-parameter Hayashi-Shirafuji model, obstructing their interpretation as black hole configurations.
Significance. If substantiated with explicit derivations, the result would be significant for assessing the viability of teleparallel equivalents of GR and related models in strong-field regimes. It would provide a concrete obstruction to black hole interpretations in these frameworks, complementing existing experimental constraints on the parameters.
major comments (2)
- [Abstract and opening paragraphs] Abstract and opening paragraphs: The central claim assumes that local horizons identified via metric null congruence expansions coincide with surfaces where the teleparallel (Weitzenböck) geometry becomes singular. However, since the connection defines parallel transport and geodesic deviation differently from the Levi-Civita connection, a metric-marginally trapped surface need not be marginally trapped in the teleparallel sense; this requires explicit verification to ensure the torsion divergence is not a coordinate or frame artifact.
- [Derivation sections] Derivation of torsion scalars: The abstract states the conclusion that divergences occur in all viable models, but without the full derivation or checks distinguishing physical singularities from coordinate artifacts (as noted in the soundness assessment), the load-bearing steps in the calculation remain unverified.
minor comments (1)
- Clarify the explicit form of the torsion scalars used in the divergence analysis and ensure all relevant equations are numbered for cross-reference.
Simulated Author's Rebuttal
We thank the referee for their careful reading of the manuscript and for raising these important points about the identification of horizons and the verification of our derivations. We address each comment below and have revised the manuscript to strengthen the presentation of our results.
read point-by-point responses
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Referee: [Abstract and opening paragraphs] The central claim assumes that local horizons identified via metric null congruence expansions coincide with surfaces where the teleparallel (Weitzenböck) geometry becomes singular. However, since the connection defines parallel transport and geodesic deviation differently from the Levi-Civita connection, a metric-marginally trapped surface need not be marginally trapped in the teleparallel sense; this requires explicit verification to ensure the torsion divergence is not a coordinate or frame artifact.
Authors: We agree that the distinction between the Levi-Civita and Weitzenböck connections merits explicit attention. Because matter couples minimally to the metric in NGR, the causal structure and local horizons are determined by metric null congruences; this is the standard approach in the teleparallel literature. In the revised manuscript we have added an explicit calculation (new subsection in Section 2) that recomputes the expansion scalars using the Weitzenböck connection directly. We show that the surfaces identified by the metric expansion coincide with the loci where the torsion scalars diverge, and that this divergence is invariant under local Lorentz transformations and under changes between common coordinate systems (Schwarzschild, Eddington-Finkelstein, and isotropic coordinates). These additions confirm that the singularity is intrinsic to the teleparallel geometry rather than a coordinate or frame artifact. revision: yes
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Referee: [Derivation sections] The abstract states the conclusion that divergences occur in all viable models, but without the full derivation or checks distinguishing physical singularities from coordinate artifacts (as noted in the soundness assessment), the load-bearing steps in the calculation remain unverified.
Authors: The step-by-step derivation of the torsion scalars for the two-parameter NGR family is given in Sections 3 and 4, beginning from the general torsion tensor constructed from the tetrad and proceeding to the three independent contractions T, T1, T2, T3. In the revised version we have expanded the presentation by (i) writing the explicit component expressions for a general spherically symmetric tetrad, (ii) evaluating the scalars at the metric horizon, and (iii) repeating the evaluation in two additional coordinate systems to demonstrate that the divergences are not removable by coordinate choice. We have also added a short appendix tabulating the leading divergent terms for the viable parameter ranges, including TEGR and the one-parameter Hayashi-Shirafuji model. These revisions make the load-bearing steps fully explicit and address the distinction between physical and coordinate singularities. revision: yes
Circularity Check
No circularity: torsion divergences derived from explicit NGR definitions and metric horizon location
full rationale
The paper starts from the standard definition of NGR as a teleparallel theory with three (normalized to two) free parameters, states that matter couples minimally to the metric so that test particles follow geodesics, and adopts the usual null-congruence expansion to locate local horizons. It then substitutes the explicit torsion expressions (built from the Weitzenböck connection and tetrads) into the scalars and evaluates them on the metric-defined horizon surface. This is a direct computation from the theory's constitutive relations and the stated geometric assumption; the divergence result is not equivalent to any input by construction, nor does it rest on a self-citation chain or a fitted parameter renamed as a prediction. The derivation remains self-contained against external benchmarks of teleparallel geometry.
Axiom & Free-Parameter Ledger
free parameters (1)
- two free parameters of NGR after normalization
axioms (2)
- domain assumption Matter couples minimally to the metric so test particles follow geodesics
- standard math Standard differential geometry and teleparallel connection definitions hold
Lean theorems connected to this paper
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IndisputableMonolith/Foundation/AlexanderDuality.leanalexander_duality_circle_linking unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
Assuming such horizons exist, we demonstrate that all physically viable NGR models... inevitably exhibit divergences in torsion scalars at the local horizon.
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IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
θ(ℓ) = √2 / A2 [ln A3]' ... local horizon at rh where θ(ℓ)(rh)=0
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Forward citations
Cited by 1 Pith paper
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On non-vacuum black holes in new general relativity
New general relativity does not admit physically meaningful non-trivial black holes distinct from those of the teleparallel equivalent of general relativity.
Reference graph
Works this paper leans on
-
[1]
R. Aldrovandi and J. G. Pereira, Fundamental Theories of Physics , Vol. 173 (Springer, Dordrecht, 2013)
work page 2013
- [2]
-
[3]
S. Bahamonde et al. , Rep. Prog. Phys. 86, 026901 (2023), arXiv:2106.13793
-
[4]
Y. F. Cai et al. , Rep. Prog. Phys. 79, 106901 (2016), arXiv:1511.07586
work page internal anchor Pith review Pith/arXiv arXiv 2016
-
[5]
Modified teleparallel gravity: inflation without inflaton
R. Ferraro and F. Fiorini, Phys. Rev. D 75, 084031 (2007), arXiv:gr-qc/0610067
work page internal anchor Pith review Pith/arXiv arXiv 2007
- [6]
-
[7]
M. Krˇ sˇ s´ ak and E. N. Saridakis, Class. Quantum Grav.33 115009, (2016)
work page 2016
-
[8]
C. Pfeifer and S. Schuster, Universe 7, 153 (2021), arXiv:2104.00116
- [9]
- [10]
-
[11]
A. Golovnev and M. J. Guzm´ an, Universe7, 121 (2021), arXiv:2103.16970
- [12]
-
[13]
S. Bahamonde et al. , Phys. Rev. D 106, 084046 (2022), arXiv:2307.14720
-
[14]
S. Bahamonde, L. Ducobu, and C. Pfeifer, J. Cosmol. Astropart. Phys. 04, 018 (2022), arXiv:2201.11445
-
[15]
Flat connection for rotating vacuum spacetimes in extended teleparallel gravity theories
L. J¨ arvet al. , Universe 5, 142 (2019), arXiv:1905.03305
work page internal anchor Pith review Pith/arXiv arXiv 2019
-
[16]
S. Bahamonde et al. , Phys. Rev. D 103, 044058 (2021), arXiv:2012.09193
-
[17]
K. Hayashi and T. Nakano, Prog. Theor. Phys. 38, 491 (1967); T. Shirafuji, ibid. 58, 353 (1977); K. Hayashi, Phys. Lett. B 69, 441 (1977)
work page 1967
- [18]
- [19]
-
[20]
F. M¨ uller-Hoissen and J. Nitsch, Phys. Rev. D 28, 718 (1983)
work page 1983
- [21]
-
[22]
J. M. Nester, Class. Quantum Grav. 5, 1003 (1988)
work page 1988
-
[23]
Revisiting stability in new general relativity,
S. Bahamonde, D. Blixt, K. F. Dialektopoulos, and A. Hell, Phys. Rev. D 111, 064080 (2025), arXiv:2404.02972 [gr-qc]
- [24]
-
[25]
A. Golovnev, A. N. Semenova, and V. P. Vandeev, J. Cosmol. Astropart. Phys. 01, 003 (2024); arXiv:2309.02853 [gr-qc]
-
[26]
A. Golovnev, Ukr. J. Phys. 69, 456 (2024); arXiv:2405.14184 [gr-qc]
-
[27]
M. Fukui and T. Shirafuji, Prog. Theor. Phys. 71, 1063 (1984); J. Masukawa and O. Miyamura, ibid. 71, 1213 (1984); M. Fukui, J. Masukawa, and S. Ogino, ibid. 76, 938 (1986)
work page 1984
- [28]
-
[29]
J. M. Nester, L. L. So, and T. Vargas, Phys. Rev. D 78, 044035 (2008), arXiv:0803.0181. 23
work page internal anchor Pith review Pith/arXiv arXiv 2008
-
[30]
A. Golovnev, A. N. Semenova, and V. P. Vandeev, J. Cosmol. Astropart. Phys. 04, 064 (2024), arXiv:2312.16021
-
[31]
K. Hayashi and T. Shirafuji, Phys. Rev. D 19, 3524 (1979); 24, 3312 (1981); Prog. Theor. Phys. 84, 36 (1990)
work page 1979
- [32]
- [33]
- [34]
-
[35]
Y. N. Obukhov and J. G. Pereira, Phys. Rev. D 67, 044016 (2003), arXiv:gr-qc/0212080
work page internal anchor Pith review Pith/arXiv arXiv 2003
-
[36]
Static spherically symmetric solutions in new general relativity,
A. Golovnev, A. N. Semenova, and V. P. Vandeev, Class. Quantum Grav. 41, 055009 (2024), arXiv:2305.03420
-
[37]
H. Asuk¨ ulaet al. , Phys. Rev. D 109, 064027 (2024), arXiv:2311.17999
- [38]
- [39]
- [40]
-
[41]
S. Bahamonde and C. Pfeifer, Int. J. Geom. Meth. Mod. Phys. 18, 2140001 (2021), arXiv:2010.02161
-
[42]
Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws
A. Ashtekar and B. Krishnan, Phys. Rev. Lett. 89, 261101 (2002), arXiv:gr-qc/0207080; Phys. Rev. D 68, 104030 (2003), arXiv:gr-qc/0308033
work page internal anchor Pith review Pith/arXiv arXiv 2002
-
[43]
A. A. Coley and D. D. McNutt, Class. Quantum Grav. 35, 025013 (2017), arXiv:1710.08773; A. A. Coley, D. D. McNutt, and A. A. Shoom, Phys. Lett. B 771, 131 (2017), arXiv:1710.08457; D. D. McNutt et al. , Gen. Relativ. Gravit. 50, 1 (2018), arXiv:1709.03362
work page internal anchor Pith review Pith/arXiv arXiv 2017
-
[44]
Geometric structure of the generic static traversable wormhole throat
D. Hochberg and M. Visser, Phys. Rev. D 56, 4745 (1997), arXiv:gr-qc/9704082
work page internal anchor Pith review Pith/arXiv arXiv 1997
-
[45]
J. D. McCrea, Class. Quantum Grav. 9, 553 (1992)
work page 1992
-
[46]
R. Aldrovandi and J. G. Pereira, An Introduction to Geometrical Physics (World Scientific, Singa- pore, 1995)
work page 1995
- [47]
-
[48]
E. Poisson, A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics (Cambridge Univer- sity Press, Cambridge, 2004)
work page 2004
-
[49]
S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, 1973)
work page 1973
-
[50]
D. F. L´ opez, Ph.D. thesis, Dalhousie University (2026), to be published. 24 Appendix A Results of the AFE perturbative analysis In this section, we summarize the results of the perturbative analysis of the AFE. For a complete and detailed treatment, refer to [50]. Note that all cases are presented here except for the case u = v = 0, which was outlined i...
work page 2026
-
[51]
b1 ≤ 0 and b2 < 3b1 4) b1 > 0 and b2 < −b1
-
[52]
b1 ≤ 0 and 0 < b 2 < −b1 5) b1 > 0 and − b1 < b 2 < 0
-
[53]
(C.17), we determine the corresponding ranges of α and β, as given in Eq
b1 ≤ 0 and b2 > −b1 6) b1 > 0 and b2 > 3b1 (C.17) Using the constraints in Eq. (C.17), we determine the corresponding ranges of α and β, as given in Eq. (C.16), for each of the previously listed cases
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[54]
1 2 < α ≤ 1 and − 1 ≤ β < 1 2 4) 1 < α < 5 4 and β < −1
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[55]
α > 2 and 5 4 < β < 2 5) 5 4 < α < 2 and β > 2
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[56]
α ≤ −1 and 1 ≤ β < 5 4 6) − 1 < α < 1 2 and 1 2 < β < 1 (C.18) 35 Furthermore, all these cases can be summarized by eliminating the square root in Eq. (C.16) and expressing one parameter directly in terms of the other: α = 4 − 5β 5 − 4β or β = 4 − 5α 5 − 4α (C.19) This explicitly shows that α and β are not independent parameters, as was already evident fr...
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[57]
1 2 < α < 4 5 or α = 1 α = 1
-
[58]
1 < α < 5 4 1 < α < 5 4
-
[59]
5 4 < α < 2 5 4 < α < 2 5 4 < α < 2
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[60]
To verify the second condition in Eq
0 < α < 1 2 Table 22: Parameter ranges of α for which θ(ℓ)(rh) = 0 holds in each case; a blank indicates that no such range exists. To verify the second condition in Eq. (31), we evaluate Eq. (C.22b) at r < r h, corresponding to a region in the neighbourhood just inside the possible AH. We then check whether the result is a real and negative number, which...
-
[61]
α = 3 2 α = 7 5 6) Table 23: Parameter values of α for which ∆ θ(ℓ)(r < r h) < 0 holds in each case; a blank indicates that no such value exists. Case r+ r−
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[62]
α = 1 α = 1 3.1) α = −1 α = −1 3.2) α < −1
-
[63]
Table 24 presents the values of α for which an AH is well defined
α = 3 2 α = 7 5 Table 24: Parameter values of α for which a well-defined AH exists in each case; a blank indicates that no such value exists. Table 24 presents the values of α for which an AH is well defined. Note that case 3) has been split into two subcases: 3.1) and 3.2). Cases 1) and 3.1) both correspond to TEGR, differing only in the values of b2 and...
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[64]
∞ ∞ ∞ ∞ ∞ ∞ 3.2) > 0 > 0 < 0
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[65]
As shown in Table 25, for case 1) we have r+ = r− = rs
> 0 > 0 > 0 > 0 > 0 < 0 Table 25: Torsion scalars evaluated at the AH, r+ and r−, for each case; a blank indicates that no AH exists to be evaluated in the corresponding case. As shown in Table 25, for case 1) we have r+ = r− = rs. Notably, case 1) is the only case in which the teleparallel scalars diverge at the apparent horizon location. It is also the ...
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[66]
and 5) fall under Type 1, which is characterized by unavoidable ghost modes and, again, does not admit TEGR as a limiting case, since in these cases b1 > 0. These results are consistent with the broader analysis presented in the main text and serve as a concrete example evaluated in a different coordinate gauge. 39
discussion (0)
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