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arxiv: 2602.12496 · v2 · submitted 2026-02-13 · 🌀 gr-qc

Recognition: 2 theorem links

· Lean Theorem

On non-vacuum black holes in new general relativity

D. F. L\'opez , A. A. Coley , B. Yildirim
Authors on Pith no claims yet

Pith reviewed 2026-05-15 23:02 UTC · model grok-4.3

classification 🌀 gr-qc
keywords new general relativityblack holesteleparallel equivalent of general relativityspherically symmetricperfect fluidelectromagnetic fieldghost instabilitiesNewtonian limit
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The pith

New general relativity does not admit physically meaningful non-trivial black holes with matter distinct from teleparallel equivalent of general relativity.

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

The paper examines static and spherically symmetric black hole configurations in new general relativity, a torsion-based modification with three free parameters. In the physically admissible parameter space that avoids ghosts, propagates a spin-2 mode, and matches the Newtonian limit, the presence of a local horizon together with a perfect fluid and electromagnetic field cannot occur. Such configurations force the parameters into regions with instabilities or other pathologies. The geometries stay regular at the horizon, indicating the problem lies in the theory's viability rather than a geometric singularity. As a result, the only allowed black hole solutions are those identical to the teleparallel equivalent of general relativity.

Core claim

In the class of models examined, the mere existence of static and spherically symmetric configurations with a local black-hole horizon in the presence of a perfect fluid and electromagnetic field forces the free parameters of new general relativity into regions associated with known pathological models: theories that either contain ghost instabilities, do not propagate a spin-2 mode, or lack a Newtonian limit. The remaining geometries are regular at the horizon, so the obstruction is not a breakdown of the geometry but a breakdown of the underlying theory. We therefore conclude that new general relativity does not admit physically meaningful non-trivial black holes distinct from those of the

What carries the argument

The three-parameter Lagrangian of new general relativity restricted to the admissible subspace (ghost-free, spin-2 propagating, Newtonian limit), together with the imposition of a local black-hole horizon in static spherically symmetric spacetimes containing a perfect fluid and electromagnetic field.

Load-bearing premise

The assumption that a local black-hole horizon exists in static and spherically symmetric configurations with a perfect fluid and electromagnetic field.

What would settle it

Finding a static spherically symmetric black hole with surrounding perfect fluid or electromagnetic field whose effective parameters remain in the ghost-free, spin-2, Newtonian region without reducing exactly to teleparallel equivalent solutions.

read the original abstract

New general relativity (NGR) is a torsion-based modification of general relativity whose Lagrangian depends on three free parameters, $(c_{a}, c_{v}, c_{t})$. A subset of the parameter space is physically admissible, namely that which simultaneously ensures ghost-freedom, propagation of a spin-2 mode, and a consistent Newtonian limit. In this work we analyze static and spherically symmetric configurations in NGR, both in vacuum and in the presence of a perfect fluid and an electromagnetic field, under the assumption of the existence of a local black-hole horizon. We find that the mere existence of such configurations forces the free parameters into regions associated with known pathological models: theories that either contain ghost instabilities, do not propagate a spin-2 mode, or lack a Newtonian limit. The remaining geometries are regular at the horizon, so the obstruction is not a breakdown of the geometry but a breakdown of the underlying theory. We therefore conclude that, within the class of models examined, NGR does not admit physically meaningful non-trivial black holes distinct from those of the teleparallel equivalent of general relativity.

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 / 2 minor

Summary. The manuscript examines static spherically symmetric configurations in New General Relativity (NGR) with Lagrangian parameters (c_a, c_v, c_t), both in vacuum and with perfect fluid plus electromagnetic field. Assuming the existence of a local black-hole horizon, it substitutes the horizon regularity condition into the NGR field equations and derives that the parameters are forced into regions that are ghost-ridden, lack a propagating spin-2 mode, or fail the Newtonian limit. Only the teleparallel equivalent of general relativity (TEGR) point remains viable, with the geometries otherwise regular at the horizon; the obstruction is therefore in the underlying theory rather than a geometric singularity.

Significance. If the central derivation holds, the result is significant because it shows that NGR does not admit physically distinct, healthy black-hole solutions beyond TEGR within the examined symmetry class and matter content. This provides a concrete obstruction in parameter space for strong-field applications of NGR and reinforces the need for viability conditions (ghost-freedom, spin-2 propagation, Newtonian limit) to be checked against exact solutions. The explicit scoping to static spherical symmetry and the location of the pathology in the parameters rather than in curvature singularities are strengths.

major comments (2)
  1. [§4] §4, after Eq. (28): the vacuum field equations for the static spherically symmetric ansatz are not written out in full before the horizon condition is imposed; only the resulting algebraic constraints on (c_a, c_v, c_t) appear. Without the intermediate steps, independent verification that the substitution yields only the TEGR point is not possible from the text alone.
  2. [§5.2] §5.2, Eqs. (51)–(53): the non-vacuum stress-energy contributions from the perfect fluid and electromagnetic field are inserted at the horizon, but the paper does not demonstrate that these components remain finite and satisfy the contracted Bianchi identities in the modified theory for any parameter choice outside TEGR. An explicit check that the TEGR limit recovers the standard Reissner–Nordström–fluid solution would confirm the claim.
minor comments (2)
  1. [§2] The admissible parameter region is referenced to earlier literature without a self-contained summary of the three viability conditions (ghost-freedom, spin-2 mode, Newtonian limit) in the present notation; a short paragraph or table would improve readability.
  2. [Figure 1] Figure 1 caption: the shading of the pathological regions is described only qualitatively; explicit boundary equations for the ghost and Newtonian-limit surfaces would make the figure self-contained.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which have helped improve the clarity of the manuscript. We address each major comment below and have revised the text accordingly to incorporate the requested details.

read point-by-point responses

  1. Referee: [§4] §4, after Eq. (28): the vacuum field equations for the static spherically symmetric ansatz are not written out in full before the horizon condition is imposed; only the resulting algebraic constraints on (c_a, c_v, c_t) appear. Without the intermediate steps, independent verification that the substitution yields only the TEGR point is not possible from the text alone.

    Authors: We agree that the intermediate steps of the derivation should be shown explicitly for independent verification. In the revised manuscript we now write out the complete set of vacuum field equations for the static spherically symmetric ansatz immediately after Eq. (28), before the horizon regularity condition is imposed. We then display the step-by-step substitution of the horizon condition into these equations, leading to the algebraic constraints on (c_a, c_v, c_t) and confirming that only the TEGR point survives. This addition makes the derivation fully transparent. revision: yes

  2. Referee: [§5.2] §5.2, Eqs. (51)–(53): the non-vacuum stress-energy contributions from the perfect fluid and electromagnetic field are inserted at the horizon, but the paper does not demonstrate that these components remain finite and satisfy the contracted Bianchi identities in the modified theory for any parameter choice outside TEGR. An explicit check that the TEGR limit recovers the standard Reissner–Nordström–fluid solution would confirm the claim.

    Authors: We thank the referee for this observation. In the revised manuscript we have expanded §5.2 to include an explicit demonstration that the perfect-fluid and electromagnetic stress-energy components remain finite at the horizon for all parameter choices outside TEGR. We further verify that these components satisfy the contracted Bianchi identities in the modified theory. In addition, we now show that the TEGR limit of the solution precisely recovers the standard Reissner–Nordström–fluid geometry, as required. These verifications are inserted immediately after Eqs. (51)–(53). revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation proceeds by direct substitution into field equations

full rationale

The paper derives its conclusion by imposing the black-hole horizon condition on the NGR field equations for static spherically symmetric spacetimes with perfect fluid and electromagnetic field. This leads to constraints on the parameters (c_a, c_v, c_t) that push them into pathological regimes. No step reduces to a fitted quantity or self-referential definition; the obstruction is located in the parameter space rather than by construction. Any self-citations are not load-bearing for the central claim, which rests on the explicit substitution into the equations.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard assumption of a local horizon in a static spherically symmetric metric plus the three Lagrangian parameters of NGR; no new entities are introduced.

free parameters (1)
  • c_a, c_v, c_t
    The three free parameters appearing in the NGR Lagrangian; admissible subsets are defined by ghost-freedom, spin-2 propagation, and Newtonian limit.
axioms (1)
  • domain assumption Existence of a local black-hole horizon in static spherically symmetric spacetime
    Invoked to classify the configurations examined in both vacuum and non-vacuum cases.

pith-pipeline@v0.9.0 · 5498 in / 1178 out tokens · 53220 ms · 2026-05-15T23:02:55.616425+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages · 7 internal anchors

  1. [1]

    Aldrovandi and J

    R. Aldrovandi and J. G. Pereira.Teleparallel Gravity: An Introduction. Vol. 173. Fundamental Theories of Physics. Springer, 2012

    work page 2012

  2. [2]

    Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach

    M. Krššák et al. “Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach”. In: Class. Quantum Grav. 36.18 (2019), p. 183001. arXiv:1810.12932 [gr-qc]

    work page arXiv 2019

  3. [3]

    Metric-affine approach to teleparallel gravity

    Y. N. Obukhov and J. G. Pereira. “Metric-Affine Approach to Teleparallel Gravity”. In: Phys. Rev. D 67.4 (2003), p. 044016. arXiv:gr-qc/0212080 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  4. [4]

    On Black Holes in Teleparallel Torsion Theories of Gravity

    A. A. Coley, N. T. Layden, and D. F. López. “On Black Holes in Teleparallel Torsion Theories of Gravity”. In: Gen. Relativ. Gravit. 57.3 (2025), p. 59. arXiv:2503.13215 [gr-qc]

    work page arXiv 2025

  5. [5]

    On black holes in new general relativity

    D. F. López, A. A. Coley, and R. J. van den Hoogen. “On Black Holes in New General Relativity”. In: Class. Quantum Grav. 42.24 (2025), p. 245011. arXiv:2508.20314 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  6. [6]

    Modified teleparallel gravity: inflation without inflaton

    R. Ferraro and F. Fiorini. “Modified Teleparallel Gravity: Inflation without an Inflaton”. In: Phys. Rev. D 75.8 (2007), p. 084031. arXiv:gr-qc/0610067 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  7. [7]

    Spherically Symmetric Teleparallel Geometries

    A. A. Coley et al. “Spherically Symmetric Teleparallel Geometries”. In: Eur. Phys. J. C 84 (2024), p. 334. arXiv:2402.07238 [gr-qc]

    work page arXiv 2024

  8. [8]

    Teleparallel Geometry with Spherical Symmetry: The Diagonal and Proper Frames

    R. J. van den Hoogen and H. Forance. “Teleparallel Geometry with Spherical Symmetry: The Diagonal and Proper Frames”. In: JCAP 2024.11 (2024), p. 033. arXiv:2408.13342 [gr-qc]

    work page arXiv 2024

  9. [9]

    General Teleparallel Modifications of Schwarzschild Geometry

    S. Bahamonde and C. Pfeifer. “General Teleparallel Modifications of Schwarzschild Geometry”. In: Int. J. Geom. Methods Mod. Phys. 18.supp01 (2021), p. 2140001. arXiv:2010.02161 [gr-qc]

    work page arXiv 2021

  10. [10]

    New General Relativity

    K. Hayashi and T. Shirafuji. “New General Relativity”. In: Phys. Rev. D 19.12 (1979), pp. 3524– 3553

    work page 1979

  11. [11]

    Addendum to “New General Relativity

    K. Hayashi and T. Shirafuji. “Addendum to “New General Relativity””. In: Phys. Rev. D 24.12 (1981), pp. 3312–3314

    work page 1981

  12. [12]

    Static, Isotropic Spacetime in New General Relativity

    K. Hayashi and T. Shirafuji. “Static, Isotropic Spacetime in New General Relativity”. In: Prog. Theor. Phys. 84.1 (1990), pp. 36–40

    work page 1990

  13. [13]

    Singularities of “Schwarzschild-Like

    T. Kawai and N. Toma. “Singularities of “Schwarzschild-Like” Space-Time in New General Rela- tivity”. In: Prog. Theor. Phys. 83.1 (1990), pp. 1–6

    work page 1990

  14. [14]

    Degrees of Freedom in Modified Teleparallel Gravity

    A. Golovnev. “Degrees of Freedom in Modified Teleparallel Gravity”. In: Ukr. J. Phys. 69.7 (2024), p. 456. arXiv:2405.14184 [gr-qc]

    work page arXiv 2024

  15. [15]

    Static Spherically Symmetric Solutions in New General Relativity

    A. Golovnev, A. N. Semenova, and V. P. Vandeev. “Static Spherically Symmetric Solutions in New General Relativity”. In: Class. Quantum Grav. 41.5 (2024), p. 055009. arXiv:2305.03420 [gr-qc]

    work page arXiv 2024

  16. [16]

    Gravitational Waves in New General Relativ- ity

    A. Golovnev, A. N. Semenova, and V. P. Vandeev. “Gravitational Waves in New General Relativ- ity”. In: JCAP 2024.01 (2024), p. 003. arXiv:2309.02853 [gr-qc]

    work page arXiv 2024

  17. [17]

    Revisiting Stability in New General Relativity

    S. Bahamonde et al. “Revisiting Stability in New General Relativity”. In: Phys. Rev. D 111.6 (2025), p. 064080. arXiv:2404.02972 [gr-qc]

    work page arXiv 2025

  18. [18]

    Non-Linear Obstructions for Consistent New Gen- eral Relativity

    J. Beltrán Jiménez and K. F. Dialektopoulos. “Non-Linear Obstructions for Consistent New Gen- eral Relativity”. In: JCAP 2020.01 (2020), p. 018. arXiv:1907.10038 [gr-qc]

    work page arXiv 2020

  19. [19]

    S. W. Hawking and G. F. R. Ellis.The Large Scale Structure of Space-Time. Cambridge University Press, 1973. 27

    work page 1973

  20. [20]

    Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws

    A. Ashtekar and B. Krishnan. “Dynamical Horizons: Energy, Angular Momentum, Fluxes, and Balance Laws”. In: Phys. Rev. Lett. 89.26 (2002), p. 261101. arXiv:gr-qc/0207080 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  21. [21]

    Dynamical Horizons and their Properties

    A. Ashtekar and B. Krishnan. “Dynamical Horizons and Their Properties”. In: Phys. Rev. D 68.10 (2003), p. 104030. arXiv:gr-qc/0308033 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  22. [22]

    Identification of black hole horizons using scalar curvature invariants

    A. A. Coley and D. D. McNutt. “Identification of Black Hole Horizons Using Scalar Curvature Invariants”. In: Class. Quantum Grav. 35.2 (2018), p. 025013. arXiv:1710.08773 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  23. [23]

    Geometric Horizons

    A. A. Coley, D. D. McNutt, and A. A. Shoom. “Geometric Horizons”. In: Phys. Lett. B 771 (2017), pp. 131–135. arXiv:1710.08457 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  24. [24]

    Cartan Invariants and Event Horizon Detection

    D. Brooks et al. “Cartan Invariants and Event Horizon Detection”. In: Gen. Relativ. Gravit. 50.4 (2018), p. 37. arXiv:1709.03362 [gr-qc]

    work page arXiv 2018

  25. [25]

    Poisson.A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics

    E. Poisson.A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics. Cambridge: Cam- bridge University Press, 2004

    work page 2004

  26. [26]

    Symmetry and Equivalence in Teleparallel Gravity

    A. A. Coley, R. J. van den Hoogen, and D. D. McNutt. “Symmetry and Equivalence in Teleparallel Gravity”. In: J. Math. Phys. 61.7 (2020), p. 072503. arXiv:1911.03893 [gr-qc]

    work page arXiv 2020

  27. [27]

    A Frame Based Approach to Computing Symmetries with Non-Trivial Isotropy Groups

    D. D. McNutt, A. A. Coley, and R. J. van den Hoogen. “A Frame Based Approach to Computing Symmetries with Non-Trivial Isotropy Groups”. In: J. Math. Phys. 64.3 (2023), p. 032503. arXiv: 2302.11493 [gr-qc]

    work page arXiv 2023

  28. [28]

    R. M. Wald.General Relativity. University of Chicago Press, 2010

    work page 2010

  29. [29]

    Bianchi Type Cosmological Models in f(T)Tele-parallel Gravity

    R. J. van den Hoogen, A. A. Coley, and D. D. McNutt. “Bianchi Type Cosmological Models in f(T)Tele-parallel Gravity”. In: JCAP 2023.10 (2023), p. 042. arXiv:2307.11475 [gr-qc]

    work page arXiv 2023

  30. [30]

    On Black Holes in Teleparallel Gravity

    D. F. López. “On Black Holes in Teleparallel Gravity”. To be published. PhD thesis. Dalhousie University, 2026. Appendix A Auxiliary functions The functionsF i introduced in (23), each depending only onA1 andA 2, are listed below: F1 =b 1[lnA 1]′′ + 2 +b 1 r2 +b 1[lnA 1]′[ln(A1/2 1 r2/A2)]′ + 2 +b 1 r [lnA 2]′ −(3−5b 1/2) 1 r2 +(1−b 1/2) (A2/r)2 , (A.1a) ...

    work page 2026