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arxiv: 2606.13635 · v1 · pith:TK3B3RN2new · submitted 2026-06-11 · 🌀 gr-qc

Geometrically Regular Black Object Solutions in Lower-Dimensional Gauss-Bonnet Gravity and Its Unimodular Extension

G. Alencar , T. M. Crispim , C. R. Muniz This is my paper

Pith reviewed 2026-06-27 05:55 UTC · model grok-4.3

classification 🌀 gr-qc
keywords regular black holesGauss-Bonnet gravitynonlinear electrodynamicsunimodular gravityblack bounceslower-dimensional gravityblack hole thermodynamics
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The pith

Lower-dimensional Einstein-Gauss-Bonnet gravity supports regular black holes and black-bounces when matter sectors are reconstructed from the field equations or via a unimodular extension.

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

The paper shows that the vacuum solution in lower-dimensional EGB gravity is singular at the origin, unlike the BTZ black hole. It reconstructs nonlinear electrodynamics Lagrangians directly from the equations to produce regular black-hole and Simpson-Visser black-bounce geometries that preserve BTZ-like asymptotics. As an alternative, a unimodular version of the theory is introduced in which standard Maxwell fields generate regular solutions through a spacetime-dependent cosmological function that mediates exchange between vacuum and matter sectors. Thermodynamic analysis reveals modified evaporation, remnant formation, phase transitions, and smooth recovery of EGB-BTZ limits for the bounce case.

Core claim

Regular compact objects are obtained in lower-dimensional EGB gravity by deriving nonlinear electrodynamics Lagrangians from the field equations or by formulating a unimodular extension in which Maxwell fields support regularity through a dynamical, spacetime-dependent cosmological function.

What carries the argument

Nonlinear electrodynamics Lagrangian obtained by solving the field equations, together with the spacetime-dependent cosmological function in the unimodular extension.

If this is right

  • Thermodynamic quantities are modified so that evaporation leads to remnant formation rather than complete disappearance.
  • Nontrivial phase transitions appear in the heat capacity and other thermodynamic potentials.
  • Black-bounce solutions recover the standard EGB-BTZ thermodynamics in the appropriate limit.
  • Curvature invariants remain finite everywhere, including at the throat or center.

Where Pith is reading between the lines

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

  • The dynamical cosmological function mechanism might extend to other higher-curvature theories where vacuum solutions are singular.
  • Thermodynamic remnants could connect to information-loss questions if the matter sector is quantized.
  • The same reconstruction technique for Lagrangians could be applied to other lower-dimensional modified gravities to test regularity.

Load-bearing premise

The nonlinear electrodynamics Lagrangians and spacetime-dependent cosmological function can be chosen or derived without introducing inconsistencies, energy-condition violations, or instabilities.

What would settle it

Explicit calculation showing that the derived nonlinear electrodynamics Lagrangians produce negative energy densities or dynamical instabilities at the regular center would falsify the claim that regularity is restored.

read the original abstract

We investigate the construction of regular compact objects in the recently proposed lower-dimensional Einstein--Gauss--Bonnet (EGB) gravity obtained through regularized dimensional reduction. Unlike the standard BTZ black hole, the corresponding vacuum EGB solution develops a genuine curvature singularity at the origin, providing an interesting setting in which higher-curvature corrections deteriorate the ultraviolet behavior of spacetime. To address this issue, we reconstruct matter sectors capable of restoring regularity while preserving the BTZ-like asymptotic structure. First, we derive regular black-hole solutions supported by nonlinear electrodynamics and determine the corresponding electromagnetic Lagrangians directly from the field equations. We then extend the analysis to Simpson--Visser black-bounce geometries, obtaining smooth throat configurations with finite curvature invariants throughout the spacetime. As an alternative regularization mechanism, we formulate a unimodular extension of lower-dimensional EGB gravity and show that standard Maxwell fields can support regular geometries through a dynamical exchange between the vacuum and matter sectors mediated by a spacetime-dependent cosmological function. We further investigate the thermodynamic properties of the regular black-hole and black-bounce solutions, showing that the matter sector modifies the evaporation process, allows for remnant formation, and produces nontrivial phase transitions. In the black-bounce case, the thermodynamic quantities smoothly recover the EGB-BTZ behavior in the appropriate limit. These results demonstrate that lower-dimensional EGB gravity provides a useful laboratory for exploring the interplay between higher-curvature corrections, regular compact objects, nonlinear electrodynamics, and unimodular gravity.

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

3 major / 1 minor

Summary. The paper claims to construct regular black-hole and black-bounce solutions in lower-dimensional Einstein-Gauss-Bonnet (EGB) gravity by deriving nonlinear electrodynamics (NED) Lagrangians directly from the field equations to restore regularity while preserving BTZ-like asymptotics, and by formulating a unimodular extension with a spacetime-dependent cosmological function that enables standard Maxwell fields to support regular geometries via dynamical vacuum-matter exchange. Thermodynamic properties are analyzed, showing modified evaporation, remnant formation, and phase transitions, with black-bounce quantities recovering EGB-BTZ limits.

Significance. If the derivations prove consistent without circularity or hidden inconsistencies, the work offers a concrete laboratory for regular compact objects in higher-curvature gravity, explicitly linking NED and unimodular mechanisms to singularity resolution and thermodynamics; the attempt to derive Lagrangians from field equations and the smooth thermodynamic recovery in the black-bounce limit are notable strengths.

major comments (3)
  1. [NED derivation] In the section deriving electromagnetic Lagrangians from the field equations (abstract and NED construction paragraphs): the inversion step to obtain L(F) from the metric ansatz implicitly assumes a single-valued function of the invariant F = F_{\mu\nu}F^{\mu\nu} that reproduces the full EOM including Bianchi identities; no explicit verification of this is reported, which is load-bearing for the claimed consistency of the regular solutions.
  2. [Unimodular extension] In the unimodular extension analysis: the spacetime-dependent cosmological function mediates energy exchange between vacuum and Maxwell sectors, yet no check is provided that the resulting effective stress-energy satisfies the dominant energy condition everywhere, undermining the physical viability of the regular geometries.
  3. [Thermodynamics] In the thermodynamic properties section: claims that the matter sector modifies evaporation and allows remnant formation rest on the derived NED Lagrangians and dynamical \Lambda(x); if these are reverse-engineered from the metric rather than independently constrained, the thermodynamic conclusions lose force.
minor comments (1)
  1. A brief recap of the regularized dimensional reduction procedure for lower-dimensional EGB would help readers, as the abstract assumes familiarity with the vacuum solution's singularity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments, which help clarify several aspects of our work. We address each major comment below and indicate where revisions will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: In the section deriving electromagnetic Lagrangians from the field equations (abstract and NED construction paragraphs): the inversion step to obtain L(F) from the metric ansatz implicitly assumes a single-valued function of the invariant F = F_{\mu\nu}F^{\mu\nu} that reproduces the full EOM including Bianchi identities; no explicit verification of this is reported, which is load-bearing for the claimed consistency of the regular solutions.

    Authors: The Lagrangians are obtained by direct substitution of the metric ansatz into the field equations and solving for L(F), ensuring by construction that the Einstein equations are satisfied. We acknowledge that an explicit verification of consistency with the Bianchi identities and single-valuedness of L(F) was not included. In the revised manuscript we will add this verification, confirming that the derived L(F) is single-valued in the relevant range of F and that the full set of equations (including Bianchi) holds identically. revision: yes

  2. Referee: In the unimodular extension analysis: the spacetime-dependent cosmological function mediates energy exchange between vacuum and Maxwell sectors, yet no check is provided that the resulting effective stress-energy satisfies the dominant energy condition everywhere, undermining the physical viability of the regular geometries.

    Authors: We agree that an explicit check of the dominant energy condition (DEC) for the effective stress-energy tensor is necessary to assess physical viability. Although the construction guarantees regularity and the correct asymptotics, the DEC was not verified in the original text. We will add this analysis in the revision, showing that the DEC holds throughout the spacetime except possibly in a small neighborhood of the origin where the matter sector dominates. revision: yes

  3. Referee: In the thermodynamic properties section: claims that the matter sector modifies evaporation and allows remnant formation rest on the derived NED Lagrangians and dynamical \Lambda(x); if these are reverse-engineered from the metric rather than independently constrained, the thermodynamic conclusions lose force.

    Authors: The NED Lagrangians and the spacetime-dependent cosmological function are obtained by solving the field equations for the chosen regular metric functions; they are therefore dynamically constrained rather than arbitrarily chosen. We will revise the relevant sections to emphasize this derivation procedure and its direct link to the thermodynamic quantities, thereby clarifying that the evaporation and remnant results follow from solutions that satisfy the equations of motion. revision: yes

Circularity Check

2 steps flagged

NED Lagrangians obtained by inverting field equations on pre-chosen regular metrics

specific steps
  1. fitted input called prediction [Abstract]
    "First, we derive regular black-hole solutions supported by nonlinear electrodynamics and determine the corresponding electromagnetic Lagrangians directly from the field equations."

    Regular metrics are selected first to eliminate the curvature singularity; the field equations are then solved for the stress-energy and inverted to produce L(F). The resulting Lagrangian is therefore fitted to the desired geometry rather than independently specified, rendering the regularity support tautological.

  2. self definitional [Abstract]
    "we formulate a unimodular extension of lower-dimensional EGB gravity and show that standard Maxwell fields can support regular geometries through a dynamical exchange between the vacuum and matter sectors mediated by a spacetime-dependent cosmological function."

    The unimodular extension is defined and introduced precisely to enable the dynamical \Lambda(x) that restores regularity; the claimed support is therefore built into the formulation of the extension itself.

full rationale

The central construction begins by positing regular metric ansatze (BTZ-like asymptotics with finite curvature at origin), substitutes into the EGB equations to extract the required T_{\mu u}, and then inverts to obtain L(F). This step makes regularity an input rather than an output. The unimodular extension is likewise introduced specifically to permit a dynamical \Lambda(x) that exchanges energy with Maxwell fields to achieve the same regularity. While the paper performs explicit calculations and thermodynamic analysis, the load-bearing matter-sector step reduces to construction by design. No self-citation chains or uniqueness theorems are invoked as external justification.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central constructions rest on the ability to reconstruct matter Lagrangians from the metric ansatz and on the validity of the regularized dimensional reduction that defines the lower-dimensional EGB theory. No machine-checked proofs or external data are provided.

free parameters (2)
  • nonlinear electrodynamics scale parameters
    Parameters in the NED Lagrangian are determined from the field equations to enforce regularity; their specific values are fitted to the chosen metric functions.
  • spacetime-dependent cosmological function
    Introduced in the unimodular extension to mediate vacuum-matter exchange; its functional form is chosen to produce regular solutions.
axioms (2)
  • domain assumption The regularized dimensional reduction procedure yields a consistent lower-dimensional EGB theory whose vacuum solution has a curvature singularity.
    Invoked in the opening paragraphs to motivate the need for matter regularization.
  • domain assumption The asymptotic BTZ-like structure must be preserved while restoring regularity at the origin.
    Stated as a requirement for the reconstructed matter sectors.

pith-pipeline@v0.9.1-grok · 5815 in / 1646 out tokens · 22146 ms · 2026-06-27T05:55:35.092514+00:00 · methodology

discussion (0)

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