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arxiv: 2601.17848 · v2 · submitted 2026-01-25 · 🌀 gr-qc

Recognition: 2 theorem links

· Lean Theorem

Three dimensional black bounces in f(R) gravity

Marcos V. de S. Silva , Manuel E. Rodrigues , C. F. S. Pereira
Authors on Pith no claims yet

Pith reviewed 2026-05-16 11:19 UTC · model grok-4.3

classification 🌀 gr-qc
keywords black bouncesf(R) gravitynonlinear electrodynamicsthree-dimensional gravityenergy conditionsscalaron mass
0
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The pith

Black-bounce geometries from general relativity remain solutions in f(R) gravity when supported by a scalar field coupled to nonlinear electrodynamics, including a new family with vanishing curvature scalar.

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

The paper tests whether black-bounce metrics known from Einstein gravity in three dimensions continue to solve the field equations when the Einstein-Hilbert term is replaced by a general f(R) function. It shows that they do for matter consisting of a scalar field interacting with nonlinear electrodynamics, and it constructs an additional class by setting the Ricci scalar to zero everywhere. The resulting f(R) models are checked for viability through the scalaron mass and the behavior of the energy conditions, which are altered by the higher-curvature contributions.

Core claim

Black-bounce spacetimes originally obtained in three-dimensional general relativity remain exact solutions within f(R) gravity once the gravitational function and the matter Lagrangian are chosen appropriately. A separate family of solutions arises when the curvature scalar is required to vanish, which restricts f(R) to a linear form plus a constant. Both classes are sustained by a scalar field nonminimally coupled to nonlinear electrodynamics, and they satisfy the modified field equations together with standard viability conditions on the scalaron.

What carries the argument

The three-dimensional black-bounce metric ansatz with a regularizing bounce function in place of the coordinate singularity, inserted into the f(R) field equations with a scalar-nonlinear-electrodynamics source.

Load-bearing premise

The metric ansatz taken from the general-relativity black-bounce solutions continues to satisfy the modified field equations once the f(R) function and matter Lagrangian are chosen appropriately.

What would settle it

Direct substitution of the black-bounce metric and the proposed matter Lagrangian into the f(R) field equations either produces an identity for every curvature component or yields a nonzero residual that cannot be canceled by any choice of f(R).

Figures

Figures reproduced from arXiv: 2601.17848 by C. F. S. Pereira, Manuel E. Rodrigues, Marcos V. de S. Silva.

Figure 1
Figure 1. Figure 1: FIG. 1. Behavior of the function [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Behavior of the function [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Behavior of the function [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Behavior of the function [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Behavior of the function [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Combinations of the stress-energy tensor components for the [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Combination of the stress-energy tensor components for the model [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Combination of the stress-energy tensor components for the model [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
read the original abstract

We investigate the existence of black bounce solutions in $2+1$ dimensions within the framework of $f(R)$ gravity. We analyze whether black bounce geometries originally obtained in general relativity can be consistently generalized to $f(R)$ theories and identify the matter sources capable of supporting such solutions. We also construct a new class of solutions by imposing a vanishing curvature scalar. In the matter sector, we consider models involving a coupling between a scalar field and nonlinear electrodynamics, while in the gravitational sector we analyze both the Starobinsky model and more general forms of $f(R)$. We further examine the viability conditions of the $f(R)$ models that give rise to these spacetimes, including the behavior of the scalaron mass. Finally, we study the associated energy conditions, in order to assess the degree of exoticity of the matter content required to sustain these black bounce solutions and how the $f(R)$ theory modifies the energy conditions.

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 paper investigates the existence of black bounce solutions in 2+1 dimensions within f(R) gravity. It demonstrates that black bounce geometries from general relativity can be generalized to f(R) theories by selecting appropriate f(R) functions (Starobinsky and general forms) and matter sources involving a scalar field coupled to nonlinear electrodynamics. A new class of solutions is constructed by imposing a vanishing curvature scalar R=0. The work includes checks on viability conditions such as scalaron mass behavior and analysis of energy conditions to assess the exoticity of the required matter.

Significance. If the constructions hold, this provides explicit analytical examples extending GR black bounce solutions to modified gravity in three dimensions, with specific matter couplings and f(R) models. The viability and energy condition analyses add physical relevance, contributing to the study of exotic spacetimes in alternative gravity theories.

major comments (2)
  1. [Solutions] The central construction retains the GR black-bounce metric ansatz and tunes f(R) and the matter Lagrangian to satisfy the modified field equations by direct substitution. While valid by construction, the paper should explicitly verify in the solutions section that all independent components of the field equations are satisfied identically for the chosen parameter values, rather than assuming the ansatz suffices without component-wise confirmation.
  2. [R=0 solutions] For the R=0 subclass, the trace equation constraint on the matter trace is used to obtain the new solutions. The paper should clarify how this constraint interacts with the full set of field equations to ensure no additional restrictions arise on the metric functions or coupling parameters.
minor comments (2)
  1. [Matter sector] Notation for the scalar-nonlinear electrodynamics coupling in the matter Lagrangian could be made more explicit to avoid ambiguity in the field equations.
  2. [Viability] The viability section would benefit from a table summarizing the parameter ranges where the scalaron mass remains positive and the model satisfies stability conditions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each point below and will revise the manuscript accordingly to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Solutions] The central construction retains the GR black-bounce metric ansatz and tunes f(R) and the matter Lagrangian to satisfy the modified field equations by direct substitution. While valid by construction, the paper should explicitly verify in the solutions section that all independent components of the field equations are satisfied identically for the chosen parameter values, rather than assuming the ansatz suffices without component-wise confirmation.

    Authors: We appreciate this suggestion for added explicitness. The solutions were obtained by substituting the metric ansatz and chosen f(R) and matter functions directly into the modified field equations, which ensures all components are satisfied identically by construction for the selected parameters. To address the comment, we will add an explicit verification paragraph in the revised solutions section confirming that each independent component of the field equations holds identically. revision: yes

  2. Referee: [R=0 solutions] For the R=0 subclass, the trace equation constraint on the matter trace is used to obtain the new solutions. The paper should clarify how this constraint interacts with the full set of field equations to ensure no additional restrictions arise on the metric functions or coupling parameters.

    Authors: We thank the referee for highlighting the need for clarification. The trace equation is one of the full set of f(R) field equations and is used to constrain the matter trace for R=0; the remaining independent components then determine the metric functions and couplings without introducing further restrictions beyond those already satisfied by the ansatz. We will add a clarifying explanation in the revised manuscript detailing this interaction and confirming consistency. revision: yes

Circularity Check

0 steps flagged

No significant circularity; explicit construction of solutions

full rationale

The paper retains the GR black-bounce metric ansatz and selects f(R) (Starobinsky or general) plus scalar-nonlinear-electrodynamics matter to satisfy the modified field equations by direct substitution. The R=0 subclass follows from imposing the trace constraint. No quantity is defined in terms of another that is then called a prediction, no fitted parameter is renamed as output, and no self-citation chain supplies the central existence claim. Viability (scalaron mass) and energy-condition checks are performed after the solutions are obtained. The derivation is therefore self-contained against the field equations and external GR benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard f(R) field equations, the GR-derived metric ansatz, and the chosen scalar-NED matter Lagrangian; no new particles or forces are postulated.

free parameters (1)
  • f(R) model parameters (e.g., alpha in Starobinsky)
    Chosen so that the field equations are satisfied for the assumed metric; values are fixed by the solution rather than fitted to external data.
axioms (2)
  • domain assumption The 2+1D black-bounce metric ansatz from general relativity remains a valid solution class in f(R) gravity
    Invoked when substituting the metric into the modified Einstein equations.
  • domain assumption The matter sector is described by a scalar field minimally coupled to nonlinear electrodynamics
    Used to source the stress-energy tensor that supports the geometry.

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Reference graph

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