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arxiv: 2605.15255 · v1 · pith:DWPME73Onew · submitted 2026-05-14 · 🌀 gr-qc

Dymnikova Black Holes in Unimodular Gravity: Maxwell Sources and Vacuum Contributions

G. Alencar , V. H. U. Borralho This is my paper

Pith reviewed 2026-05-19 16:12 UTC · model grok-4.3

classification 🌀 gr-qc
keywords Dymnikova black holeunimodular gravityregular black holesMaxwell electrodynamicsradial cosmological constantvacuum contributionsasymptotically neutral
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The pith

Dymnikova regular black holes arise from standard Maxwell electrodynamics in unimodular gravity with a radially varying cosmological term.

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

The paper examines the Dymnikova regular black hole within unimodular gravity and shows how the vacuum sector regularizes the geometry. By allowing a controlled violation of the covariant conservation of the energy-momentum tensor, the cosmological constant emerges as a radial-dependent function. The central result is that the same geometry can be generated by ordinary Maxwell sources, yielding a regular electric field from a localized charge distribution that carries zero net charge at infinity.

Core claim

The Dymnikova spacetime can be consistently realized as a solution of unimodular gravity sourced by standard Maxwell electrodynamics together with a radial-dependent cosmological contribution. In this construction the electric field remains finite everywhere and corresponds to a localized charge whose integral vanishes asymptotically, so the spacetime does not behave as an asymptotically charged object.

What carries the argument

Unimodular gravity framework in which a controlled non-conservation of the energy-momentum tensor generates a radial-dependent cosmological term Lambda(r) that regularizes the geometry while permitting Maxwell electrodynamics to support the Dymnikova metric.

Load-bearing premise

The covariant conservation law for the energy-momentum tensor can be violated in a controlled manner to allow the cosmological term to depend on radius.

What would settle it

Compute the electromagnetic field and sources implied by the Dymnikova metric in unimodular gravity and check whether they satisfy the standard Maxwell equations with a charge density whose total integral is zero at spatial infinity.

read the original abstract

In this work, we investigate the Dymnikova regular black hole within the framework of unimodular gravity, emphasizing the role of the effective vacuum sector in the regularization of the geometry. By allowing a controlled violation of the covariant conservation of the energy--momentum tensor, the cosmological contribution emerges dynamically as a radial-dependent function, $\Lambda=\Lambda(r)$. We first reinterpret the Dymnikova spacetime as a charged configuration supported by nonlinear electrodynamics and derive the corresponding electric and magnetic sources. Subsequently, we demonstrate that the same geometry can be consistently generated by standard Maxwell electrodynamics in unimodular gravity. In this construction, the resulting electric field is everywhere regular and corresponds to a localized charge distribution with vanishing asymptotic charge, indicating that the spacetime does not behave as an asymptotically charged object.

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 investigates the Dymnikova regular black hole metric in unimodular gravity. It first reinterprets the geometry as sourced by nonlinear electrodynamics, then claims to show that the identical spacetime can be generated using standard Maxwell electrodynamics together with a radially dependent effective cosmological term Λ(r) that arises dynamically from a controlled violation of the covariant conservation of the energy-momentum tensor. The resulting electric field is regular and corresponds to a localized charge distribution whose total charge vanishes at spatial infinity.

Significance. If the central construction is shown to be internally consistent, the result supplies a concrete example of a regular black-hole geometry sourced by linear Maxwell fields inside unimodular gravity, with the vacuum contribution emerging as a function of radius rather than being imposed by hand. The vanishing asymptotic charge is a distinctive feature that could be tested against standard asymptotically flat charged solutions.

major comments (2)
  1. [Section deriving sources in unimodular gravity] The central claim requires that the Maxwell stress-energy tensor, when inserted into the trace-free unimodular equations for the Dymnikova curvature, produces a divergence that is exactly absorbed by a consistent ∇Λ(r) while the Maxwell equations themselves remain satisfied. The manuscript must exhibit this algebraic identity explicitly (e.g., in the section deriving the effective vacuum term) rather than asserting a “controlled violation.”
  2. [Derivation of Λ(r)] Eq. (definition of Λ(r)): it is not shown that the radial dependence obtained from the trace-free projection reproduces the precise Ricci scalar and curvature invariants of the Dymnikova metric once the Maxwell contribution is subtracted. A direct substitution check is needed to confirm that no residual inconsistency remains.
minor comments (2)
  1. [Introduction] The distinction between the effective, position-dependent Λ(r) and the standard cosmological constant should be emphasized in the notation and introductory paragraphs to avoid confusion for readers familiar with unimodular gravity literature.
  2. [Results section] A brief comparison table of the electric-field profiles obtained from nonlinear electrodynamics versus the Maxwell-unimodular construction would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. The two major comments identify places where explicit algebraic verifications would strengthen the presentation of the central construction. We agree that these checks are necessary and will incorporate them in the revised manuscript.

read point-by-point responses

  1. Referee: [Section deriving sources in unimodular gravity] The central claim requires that the Maxwell stress-energy tensor, when inserted into the trace-free unimodular equations for the Dymnikova curvature, produces a divergence that is exactly absorbed by a consistent ∇Λ(r) while the Maxwell equations themselves remain satisfied. The manuscript must exhibit this algebraic identity explicitly (e.g., in the section deriving the effective vacuum term) rather than asserting a “controlled violation.”

    Authors: We agree that an explicit demonstration is required. In the revised manuscript we will add a dedicated calculation in the section on the effective vacuum term. We will compute the covariant divergence of the Maxwell stress-energy tensor for the regular electric field obtained from the Dymnikova metric, show that it equals the appropriate multiple of ∇Λ(r) required by the trace-free unimodular equations, and verify that the Maxwell equations ∇_μ F^{μν}=0 and ∇_μ *F^{μν}=0 continue to hold. This will replace the previous assertion with a direct algebraic identity. revision: yes

  2. Referee: [Derivation of Λ(r)] Eq. (definition of Λ(r)): it is not shown that the radial dependence obtained from the trace-free projection reproduces the precise Ricci scalar and curvature invariants of the Dymnikova metric once the Maxwell contribution is subtracted. A direct substitution check is needed to confirm that no residual inconsistency remains.

    Authors: We accept that a direct substitution verification is needed. In the revised version we will perform and display the explicit check: starting from the Dymnikova curvature tensors, we subtract the Maxwell contribution (using the trace-free projection), insert the derived Λ(r), and confirm that the Ricci scalar and the relevant curvature invariants are recovered without residual terms. The calculation will be presented immediately after the definition of Λ(r). revision: yes

Circularity Check

0 steps flagged

No circularity: reinterpretation of known metric in unimodular setting remains self-contained

full rationale

The paper starts from the established Dymnikova geometry and solves for the matter sources (Maxwell EMT plus effective radial Λ(r)) that reproduce it inside the trace-free unimodular equations. This is a standard source-finding procedure rather than a closed loop in which a fitted parameter or self-cited uniqueness theorem is renamed as a prediction. No equations are shown to reduce by construction to their own inputs, and the controlled violation of ∇·T is introduced as an explicit modeling choice whose consistency with the geometry is checked rather than assumed a priori. The construction therefore adds independent content about the form of the electric field and the vanishing asymptotic charge.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the Dymnikova metric as a valid regular solution and on the unimodular-gravity framework that permits a radially dependent cosmological term; no new particles or forces are postulated.

axioms (1)
  • domain assumption Unimodular gravity permits a controlled violation of covariant conservation of the energy-momentum tensor
    Invoked to allow Lambda to become a function of radius.

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Reference graph

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