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arxiv: 2604.15758 · v1 · submitted 2026-04-17 · 🌀 gr-qc · astro-ph.HE· hep-th

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Geometrically Regular Black Holes with Hedgehog Scalar Hair

Sebastian Bahamonde
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Pith reviewed 2026-05-10 08:26 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HEhep-th
keywords scalarblackholescontinuousgeometricallyhairhedgehogregular
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The pith

A continuous family of asymptotically flat, geometrically regular black holes with hedgehog scalar hair exists in a minimally coupled GR-scalar-three-form theory.

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

General relativity usually predicts black holes with a singularity where curvature becomes infinite. This work adds a special kind of scalar field arranged in a hedgehog pattern and an auxiliary three-form field that does not propagate. Under spherical symmetry, the equations admit exact solutions that stay smooth in their geometry all the way to the center. The interior looks like de Sitter space, and far away the metric is almost the same as the classic Schwarzschild black hole, with the first difference appearing only at order 1 over r to the fourth. The solutions depend on a continuous parameter in addition to mass, yet they carry no ordinary scalar charge.

Core claim

Within a spherically symmetric hedgehog ansatz, the theory admits a continuous exact family of asymptotically flat geometrically regular black holes.

Load-bearing premise

The spherically symmetric hedgehog ansatz for the scalar triplet together with the specific choice of kinetic function that yields the de Sitter core and r^{-4} correction.

Figures

Figures reproduced from arXiv: 2604.15758 by Sebastian Bahamonde.

Figure 1
Figure 1. Figure 1: FIG. 1: Metric profiles [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Inner and outer horizon radii of the [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Dimensionless density and pressures for the [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
read the original abstract

We study a simple theory based on general relativity, minimally coupled to a constrained scalar triplet and to an auxiliary non-propagating three-form sector. Within a spherically symmetric hedgehog ansatz, the theory admits a continuous exact family of asymptotically flat geometrically regular black holes. For a simple choice of kinetic function, the solutions possess a de Sitter core and approach Schwarzschild with the first correction appearing only at order $r^{-4}$. We analyse their horizon structure, thermodynamics, and main strong-field properties. The black holes carry topological scalar hair and a continuous secondary parameter, but no scalar charge. The regularity established here is geometric: the curvature invariants remain finite, although the matter sector is not completely smooth at the centre.

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.

Circularity Check

0 steps flagged

No significant circularity; solutions derived directly from field equations under ansatz

full rationale

The paper constructs solutions by imposing a spherically symmetric hedgehog ansatz on a minimally coupled scalar triplet plus auxiliary three-form in GR, then solving the resulting ODEs for a chosen kinetic function that produces the de Sitter core and r^{-4} falloff. The central claim (continuous exact family of asymptotically flat, geometrically regular black holes) follows from integrating those equations; curvature invariants are shown finite by direct computation rather than by redefinition or fit. No load-bearing step reduces to a self-citation chain, a fitted parameter renamed as prediction, or an ansatz smuggled via prior work. The construction is self-contained against the stated assumptions and external benchmarks such as asymptotic flatness and horizon structure.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 2 invented entities

The construction rests on the Einstein-Hilbert action plus minimal coupling to a constrained scalar triplet and auxiliary three-form; the hedgehog ansatz and a specific kinetic function are introduced to obtain the family.

free parameters (1)
  • kinetic function parameter
    A simple choice of kinetic function is used to obtain the de Sitter core and r^{-4} correction; its explicit form and any free constants are not stated in the abstract.
axioms (2)
  • standard math General relativity with minimal coupling
    The starting point is the Einstein-Hilbert action minimally coupled to the scalar and three-form sectors.
  • domain assumption Spherically symmetric hedgehog ansatz
    All solutions are obtained under this symmetry reduction for the scalar triplet.
invented entities (2)
  • constrained scalar triplet no independent evidence
    purpose: Provides the topological hair and enables regular geometries
    A new matter sector introduced in the theory; no independent evidence outside the model is given.
  • auxiliary non-propagating three-form no independent evidence
    purpose: Auxiliary sector to support the solutions
    Introduced as part of the theory; no independent falsifiable prediction outside the paper.

pith-pipeline@v0.9.0 · 5411 in / 1444 out tokens · 47739 ms · 2026-05-10T08:26:26.105218+00:00 · methodology

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Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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  2. Families of regular spacetimes and energy conditions

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  3. (Super-)renormalizable hairy meronic black holes

    hep-th 2026-04 unverdicted novelty 6.0

    Analytical black hole solutions are constructed in Einstein-Maxwell-Yang-Mills theory with conformally coupled scalars, generalizing MTZ and AC solutions by including non-Abelian gauge fields determined by horizon curvature.

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