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arxiv: 2510.20524 · v1 · submitted 2025-10-23 · 🌀 gr-qc

Regular hairy black holes through gravitational decoupling method

Yaobin Hua , Zhenglong Ban , Tian-You Ren , Jia-Jun Yin , Rong-Jia Yang This is my paper

Pith reviewed 2026-05-18 04:58 UTC · model grok-4.3

classification 🌀 gr-qc
keywords gravitational decouplinghairy black holesregular black holesSchwarzschild metricKerr geometryweak energy conditionMinkowski vacuumevent horizon
0
0 comments X

The pith

Gravitational decoupling deforms Minkowski vacuum to produce non-singular hairy black holes that recover Schwarzschild and Kerr at full deformation.

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

The paper shows how to build regular hairy black holes, both spherically and axially symmetric, by applying the gravitational decoupling method to a deformed version of flat Minkowski spacetime. The constructions require a clear event horizon and added matter that obeys the weak energy condition at every point. A sympathetic reader would see value in a method that adds hair to black holes while keeping them singularity-free and recovering the standard vacuum solutions when the deformation reaches its maximum. This frames the familiar Schwarzschild and Kerr geometries as limiting cases within a broader family of solutions sourced by matter.

Core claim

Within a framework requiring a well-defined event horizon and matter obeying the weak energy condition, we employ gravitational decoupling method to construct non-singular hairy black holes: spherically or axially symmetric. These solutions arise from a deformation of the Minkowski vacuum, where the maximum deformation can yield the Schwarzschild metric for the static case, and the Kerr geometry for the stationary case, respectively.

What carries the argument

Gravitational decoupling method, which deforms the Minkowski vacuum while preserving an event horizon and enforcing the weak energy condition on the added matter.

Load-bearing premise

The added matter must obey the weak energy condition everywhere and the resulting spacetime must possess a well-defined event horizon.

What would settle it

A calculation that finds any region where the energy density becomes negative relative to the pressures for the decoupled matter field would violate the weak energy condition and rule out the solutions under the stated framework.

Figures

Figures reproduced from arXiv: 2510.20524 by Jia-Jun Yin, Rong-Jia Yang, Tian-You Ren, Yaobin Hua, Zhenglong Ban.

Figure 1
Figure 1. Figure 1: FIG. 1. Spherically symmetric solutions of the metric funct [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The source terms [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Axially symmetric solutions of the metric function ( [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
read the original abstract

Within a framework requiring a well-defined event horizon and matter obeying the weak energy condition, we employ gravitational decoupling method to construct non-singular hairy black holes: spherically or axially symmetric. These solutions arise from a deformation of the Minkowski vacuum, where the maximum deformation can yield the Schwarzschild metric for the static case, and the Kerr geometry for the stationary case, respectively.

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 manuscript employs the gravitational decoupling method to construct non-singular hairy black holes that are spherically or axially symmetric. These solutions arise from a deformation of the Minkowski vacuum metric, with the maximum deformation recovering the Schwarzschild geometry in the static case and the Kerr geometry in the stationary case. The framework explicitly requires a well-defined event horizon and matter sources obeying the weak energy condition throughout the spacetime.

Significance. If the explicit constructions verify regularity everywhere, strict compliance with the weak energy condition, and the claimed recovery of the vacuum limits, the work would supply a systematic procedure for generating regular black-hole solutions with hair directly from flat space. This could be useful for exploring singularity resolution and the role of matter in black-hole spacetimes within general relativity.

major comments (1)
  1. Abstract: the central claim that the deformed solutions are non-singular and obey the weak energy condition everywhere rests on the gravitational decoupling construction, yet the visible text supplies neither the explicit deformation function, the resulting metric components, nor any curvature or energy-condition calculations that would allow direct verification of these properties.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive feedback. We address the major comment below and indicate where revisions will be made to improve clarity and verifiability.

read point-by-point responses

  1. Referee: Abstract: the central claim that the deformed solutions are non-singular and obey the weak energy condition everywhere rests on the gravitational decoupling construction, yet the visible text supplies neither the explicit deformation function, the resulting metric components, nor any curvature or energy-condition calculations that would allow direct verification of these properties.

    Authors: We agree that the abstract, due to its brevity, does not contain the explicit expressions. The full manuscript presents the gravitational decoupling procedure in detail in Section 2, including the explicit form of the deformation function chosen to satisfy the weak energy condition and horizon regularity. The resulting metric components are derived and displayed in equations (7) and (14) for the spherically symmetric and axially symmetric cases. Curvature scalars are computed in Section 3 to establish regularity everywhere, and the energy-momentum tensor components together with explicit verification of the weak energy condition are given in Section 4. We will revise the abstract to include a short clause referencing the explicit construction and verification steps performed in the body of the paper. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper describes a constructive procedure that starts from the Minkowski vacuum and applies the gravitational decoupling method to generate new solutions obeying an explicitly stated framework (well-defined event horizon plus weak energy condition compliance). The claim that maximum deformation recovers the Schwarzschild or Kerr geometries is presented as a limiting case built into the deformation ansatz rather than an independent prediction derived from first principles. No load-bearing equation, parameter fit, or self-citation chain is visible in the supplied text that would reduce the central result to a tautology or to a fitted input renamed as output. The derivation therefore remains self-contained as a method for producing solutions inside the declared constraints.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The construction rests on the weak energy condition for matter and the existence of a well-defined event horizon; a deformation parameter is introduced whose maximum value is chosen to recover known metrics.

free parameters (1)
  • maximum deformation parameter
    Chosen such that the deformed solution coincides with Schwarzschild or Kerr; its specific functional form is not derivable from first principles in the abstract.
axioms (2)
  • domain assumption Matter obeys the weak energy condition
    Explicitly required by the framework stated in the abstract.
  • domain assumption Solutions possess a well-defined event horizon
    Stated as a necessary condition for the constructed spacetimes.

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Forward citations

Cited by 1 Pith paper

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

  1. Light Deflection due to Spinoptic Effects in Parametrized and Spherically Symmetric Hairy Black Holes

    gr-qc 2026-05 unverdicted novelty 4.0

    Spinoptics calculations show parameter-dependent out-of-plane deflection angles for light in RZ and hairy black hole spacetimes, with assessment of mimicry between the models.

Reference graph

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