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arxiv: 2606.22121 · v1 · pith:IAT4TDI3new · submitted 2026-06-20 · 🌀 gr-qc

Horizon Singularities in the Schwarzschild Geometry of the Teleparallel Equivalent of General Relativity

D. F. L\'opez , A. A. Coley , R. J. van den Hoogen This is my paper

Pith reviewed 2026-06-26 11:37 UTC · model grok-4.3

classification 🌀 gr-qc
keywords teleparallel gravitySchwarzschild solutionhorizon singularitiestorsion scalarsblack hole spacetimesLorentz sectorTEGR
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The pith

In teleparallel gravity, Schwarzschild solutions split into regular and singular classes at the horizon according to the Lorentz sector.

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

The paper shows that Schwarzschild geometries in the teleparallel equivalent of general relativity divide into two subclasses set by the Lorentz sector, which comprises the tetrad and spin connection parts that affect torsion but not the metric. In the regular subclass, torsion scalar invariants stay finite at the horizon so that the horizon belongs to the manifold and a black hole interpretation holds. In the singular subclass, the invariants diverge and the horizon is excluded. The work establishes this split using three independent methods and clarifies that inertial effects alone do not cause the singularities.

Core claim

Schwarzschild TEGR geometries split into two distinct subclasses determined by the Lorentz sector of the geometry—the elements of the tetrad and spin connection not encoded in the metric but appearing in the torsion. In the regular subclass, the divergences are absent and the horizon belongs to the manifold, supporting a consistent black hole interpretation. In the singular subclass, the divergences are genuine and the horizon is excluded from the manifold. The horizon singularities are independent of the inertial structure of the frame, and the complete class of Lorentz sector functions compatible with a regular horizon is identified.

What carries the argument

The Lorentz sector of the geometry, consisting of the tetrad and spin connection elements not encoded in the metric but appearing in the torsion, which determines whether torsion scalar invariants diverge at the horizon.

If this is right

  • All torsion scalar invariants remain finite at the horizon in the regular subclass.
  • Analytic extensions across the horizon are admitted for the regular subclass.
  • The proper frame does not by itself remove inertial contributions to the torsion.
  • Horizon singularities persist independently of the inertial structure of the frame.

Where Pith is reading between the lines

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

  • The same Lorentz-sector classification may apply to other exact solutions in teleparallel gravity beyond Schwarzschild.
  • Frame choices that produce the regular class could be used to construct globally regular manifold models in numerical teleparallel simulations.
  • The independence from inertial structure suggests that metric-equivalent frames can still produce different global properties in torsion-based theories.

Load-bearing premise

That the Lorentz sector alone fixes whether horizon divergences appear in the torsion scalar invariants and that the three approaches fully classify the regular cases.

What would settle it

A explicit computation of a torsion scalar invariant that diverges at the horizon for a Lorentz sector function identified as regular by the three methods.

read the original abstract

Certain torsion scalar invariants are known to diverge at the horizon of the Schwarzschild solution in the Teleparallel Equivalent of General Relativity (TEGR), obstructing its interpretation as a black hole spacetime. We show that Schwarzschild TEGR geometries split into two distinct subclasses determined by the Lorentz sector of the geometry -- the elements of the tetrad and spin connection not encoded in the metric but appearing in the torsion. In the regular subclass, the divergences are absent and the horizon belongs to the manifold, supporting a consistent black hole interpretation. In the singular subclass, the divergences are genuine and the horizon is excluded from the manifold. As part of this analysis, we clarify the role of inertial contributions in teleparallel gravity, showing that the proper frame does not, by itself, eliminate inertial effects and that the horizon singularities are independent of the inertial structure of the frame. Using three independent approaches -- the inertial frame condition, horizon-penetrating coordinates, and the horizon regularity criterion -- we determine the complete class of Lorentz sector functions compatible with a regular horizon in Schwarzschild TEGR geometries. For this class, all torsion scalar invariants remain finite at the horizon and analytic extensions across it are admitted.

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

1 major / 0 minor

Summary. The paper claims that Schwarzschild TEGR geometries split into two distinct subclasses determined by the Lorentz sector (tetrad and spin connection elements not encoded in the metric). In the regular subclass, torsion scalar invariants remain finite at the horizon, the horizon belongs to the manifold, and analytic extensions are admitted, supporting a consistent black hole interpretation. In the singular subclass, divergences are genuine and the horizon is excluded. The authors use three approaches (inertial frame condition, horizon-penetrating coordinates, horizon regularity criterion) to determine the complete class of compatible Lorentz sector functions and clarify that inertial contributions do not cause the singularities.

Significance. If the classification holds, the result is significant for teleparallel gravity because it resolves a known obstruction to black-hole interpretations of the Schwarzschild solution in TEGR by showing that horizon divergences in torsion invariants are not intrinsic but depend on the choice of Lorentz sector. The explicit determination of the regular class and the demonstration that the proper frame does not by itself remove inertial effects provide a concrete way to select physically viable frames. The use of three listed approaches, if shown to be independent, adds robustness to the partition.

major comments (1)
  1. [Abstract] Abstract: the claim that the three approaches are independent and exhaustive for identifying the complete regular class is load-bearing for the central result, yet the abstract provides no explicit comparison or proof that the resulting sets of Lorentz sector functions coincide without gaps or redundancy; this must be demonstrated in a dedicated section or appendix with the explicit functions obtained from each method.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the importance of explicitly demonstrating the equivalence of the three approaches. We address the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the three approaches are independent and exhaustive for identifying the complete regular class is load-bearing for the central result, yet the abstract provides no explicit comparison or proof that the resulting sets of Lorentz sector functions coincide without gaps or redundancy; this must be demonstrated in a dedicated section or appendix with the explicit functions obtained from each method.

    Authors: We agree that an explicit side-by-side comparison strengthens the central claim. Sections 3–5 of the manuscript already derive the identical class of Lorentz-sector functions (those for which all torsion scalar invariants remain finite at the horizon) via the inertial-frame condition, horizon-penetrating coordinates, and the horizon-regularity criterion, respectively; the derivations are shown to be independent because each begins from a distinct geometric requirement and none presupposes the others. Nevertheless, to make the equivalence fully transparent, we will add a dedicated appendix that (i) tabulates the explicit functional forms obtained from each method, (ii) proves set equality by direct substitution, and (iii) confirms the absence of gaps or redundant solutions. We will also revise the abstract to state that the equivalence is established in the new appendix. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper conducts an explicit geometric classification of Schwarzschild TEGR solutions by examining the Lorentz sector (tetrad and spin connection components) and computing torsion scalar invariants at the horizon. The regular subclass is identified by direct verification that invariants remain finite under three listed coordinate and frame conditions; these conditions are applied as independent selection criteria rather than being fitted to or defined by the target regularity property. No parameter is tuned to data and then relabeled as a prediction, no uniqueness theorem is imported from self-citation to force the split, and the derivation does not reduce any claimed result to its own inputs by construction. The analysis is therefore self-contained against external geometric benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, ad-hoc axioms, or invented entities beyond the standard framework of TEGR and differential geometry.

pith-pipeline@v0.9.1-grok · 5753 in / 1196 out tokens · 31765 ms · 2026-06-26T11:37:57.125493+00:00 · methodology

discussion (0)

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Reference graph

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