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arxiv: 2605.08205 · v1 · submitted 2026-05-06 · 🌀 gr-qc · hep-th

Recognition: 2 theorem links

· Lean Theorem

Analytical solution of traversable wormholes in the presence of positive cosmological constant

Rajesh Karmakar, Xian-Hui Ge

Authors on Pith no claims yet

Pith reviewed 2026-05-12 01:40 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords traversable wormholesgravitational decouplingEllis-Bronnikov wormholepositive cosmological constantnull energy conditionflare-out conditiontidal forces
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The pith

An analytical traversable wormhole solution is obtained for positive cosmological constant using gravitational decoupling.

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

This paper develops an analytical model of a traversable wormhole incorporating a positive cosmological constant. It applies the gravitational decoupling method to the Ellis-Bronnikov wormhole geometry to add the Lambda term, which deforms the standard throat and introduces a cosmological throat. The resulting spacetime satisfies the flare-out condition at both throats and violates the null energy condition in their vicinity, as required to keep wormholes open. Tidal forces are evaluated to place limits on the speed needed for safe passage. The geometry exhibits modified asymptotic behavior instead of standard de Sitter asymptotics.

Core claim

We obtain an analytical solution describing a traversable WH for Λ>0 by utilizing the gravitational decoupling (GD) method. In this framework, we consider the Ellis-Bronnikov WH geometry and derive the corresponding deformation induced by the cosmological constant term. In addition to modifying the standard WH throat, this contribution leads to a cosmological throat. The resulting configuration, however, is not asymptotically de Sitter, instead, it exhibits modified asymptotic behaviour. Nevertheless, we verify that the flare-out condition holds at both throats and find violation of the null energy condition in their vicinity, as required for traversable WHs. Traversability is further tested

What carries the argument

Gravitational decoupling method applied to the Ellis-Bronnikov wormhole metric, which produces a deformation incorporating the positive cosmological constant while retaining the two-throat structure.

Load-bearing premise

The gravitational decoupling method can be applied to the Ellis-Bronnikov geometry to incorporate the positive cosmological constant term while preserving the required properties for traversability without introducing inconsistencies in the asymptotic behavior.

What would settle it

Direct substitution of the derived metric functions into the Einstein equations with positive Lambda to verify exact satisfaction, or explicit calculation showing whether the flare-out condition fails at the cosmological throat.

Figures

Figures reproduced from arXiv: 2605.08205 by Rajesh Karmakar, Xian-Hui Ge.

Figure 1
Figure 1. Figure 1: FIG. 1. The variation of the throat size for the dS-WH with [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The embedding diagram of the two dimensional sec [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The constraint on the velocity of the traveler near [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

The construction of traversable wormholes (WHs) with a cosmological constant, $\Lambda$, introduces significant challenges and leads to non-trivial modifications of the spacetime geometry. In this work, we obtain an analytical solution describing a traversable WH for $\Lambda>0$ by utilizing the gravitational decoupling (GD) method. In this framework, we consider the Ellis-Bronnikov WH geometry and derive the corresponding deformation induced by the cosmological constant term. In addition to modifying the standard WH throat, this contribution leads to a cosmological throat. The resulting configuration, however, is not asymptotically de Sitter, instead, it exhibits modified asymptotic behaviour. Nevertheless, we verify that the flare-out condition holds at both throats and find violation of the null energy condition in their vicinity, as required for traversable WHs. Traversability is further analyzed by evaluating tidal forces and deriving constraints on the velocity required for safe human passage.

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 claims to derive an analytical traversable wormhole solution for positive cosmological constant Λ by applying the gravitational decoupling method to the Ellis-Bronnikov geometry. This produces a deformed metric with both a standard wormhole throat and an additional cosmological throat; the authors state that the spacetime is not asymptotically de Sitter but exhibits modified asymptotics, while verifying the flare-out condition and null energy condition violation at both throats and analyzing traversability via tidal forces and velocity bounds.

Significance. If consistent with the Einstein equations, the work supplies a rare explicit analytical example of a traversable wormhole in the presence of positive Λ, obtained via gravitational decoupling. The explicit checks for flare-out and NEC violation, together with the traversability analysis, constitute reproducible strengths that could serve as a concrete model for further investigation of wormhole geometries with cosmological terms.

major comments (2)
  1. [§5] §5 (asymptotic behaviour paragraph): The statement that the configuration 'is not asymptotically de Sitter' but instead 'exhibits modified asymptotic behaviour' appears inconsistent with the Einstein equations containing a positive cosmological constant. Once matter sources decay, the geometry must reduce to the de Sitter (or Schwarzschild–de Sitter) vacuum; a persistent deviation implies either that the decoupled source fails to fall off or that the effective Λ term is not correctly realized. Please supply the explicit large-r expansion of the metric functions and demonstrate that it satisfies the vacuum Einstein equations with Λ > 0.
  2. [§3] §3 (derivation of the deformed metric): The gravitational decoupling procedure that adds the Λ term to the Ellis-Bronnikov seed must be shown to preserve the Einstein equations without introducing extraneous sources. Explicit expressions for the deformation function, the resulting energy-momentum tensor, and verification that it equals the original matter plus the cosmological term are required to confirm the construction is load-bearing for the claimed solution.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'modified asymptotic behaviour' is used without specifying the leading-order form; a single sentence describing the large-r metric would improve clarity for readers.
  2. [Throughout] Notation: ensure the shape function and redshift function are denoted consistently between the seed Ellis-Bronnikov metric and the decoupled solution throughout the text and equations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment point by point below, providing clarifications and committing to revisions that strengthen the presentation of our results without altering the core findings.

read point-by-point responses

  1. Referee: [§5] §5 (asymptotic behaviour paragraph): The statement that the configuration 'is not asymptotically de Sitter' but instead 'exhibits modified asymptotic behaviour' appears inconsistent with the Einstein equations containing a positive cosmological constant. Once matter sources decay, the geometry must reduce to the de Sitter (or Schwarzschild–de Sitter) vacuum; a persistent deviation implies either that the decoupled source fails to fall off or that the effective Λ term is not correctly realized. Please supply the explicit large-r expansion of the metric functions and demonstrate that it satisfies the vacuum Einstein equations with Λ > 0.

    Authors: We appreciate the referee highlighting this point for clarification. The gravitational decoupling applied to the Ellis-Bronnikov seed produces a deformation whose associated source does not decay completely at large distances, which is the origin of the modified asymptotic behavior reported in the paper. In the revised manuscript we will add the explicit large-r expansions of the metric functions and verify that they satisfy the Einstein equations with positive Λ, with the residual source contribution from the decoupling procedure explicitly identified. This will demonstrate consistency with the field equations while preserving the distinction from pure de Sitter asymptotics. revision: yes

  2. Referee: [§3] §3 (derivation of the deformed metric): The gravitational decoupling procedure that adds the Λ term to the Ellis-Bronnikov seed must be shown to preserve the Einstein equations without introducing extraneous sources. Explicit expressions for the deformation function, the resulting energy-momentum tensor, and verification that it equals the original matter plus the cosmological term are required to confirm the construction is load-bearing for the claimed solution.

    Authors: We thank the referee for requesting these explicit details. In the revised manuscript we will present the explicit form of the deformation function f(r), the full components of the resulting energy-momentum tensor, and a direct verification that the total tensor is precisely the sum of the original Ellis-Bronnikov matter and the cosmological-constant contribution. This will confirm that the gravitational decoupling procedure preserves the Einstein equations without extraneous sources. revision: yes

Circularity Check

0 steps flagged

No circularity: construction from known seed via GD is independent

full rationale

The paper starts from the established Ellis-Bronnikov wormhole metric as seed and applies the gravitational decoupling procedure to incorporate a positive cosmological constant term, yielding an explicit deformed metric with two throats. This is a direct construction whose output metric is not defined in terms of its own derived properties (no self-definitional loop), nor does any central claim reduce to a fitted parameter renamed as prediction. The GD method is an external technique (cited from prior literature by other authors), and the flare-out/NEC checks are performed on the resulting explicit functions rather than being imposed by construction. The noted non-de Sitter asymptotics is a consistency question external to the derivation chain itself and does not create circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the applicability of the gravitational decoupling method to modify the Ellis-Bronnikov geometry with a positive cosmological constant term.

axioms (1)
  • domain assumption The Ellis-Bronnikov wormhole geometry serves as a valid base spacetime for gravitational decoupling to incorporate the cosmological constant.
    Explicitly used as the starting point for deriving the deformed solution.

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