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arxiv: 2411.10804 · v2 · submitted 2024-11-16 · 🌀 gr-qc

Gravitational lensing and deflection angles of generalised Ellis-Bronnikov wormhole embedded in a warped braneworld background

Soumya Jana , Vivek Sharma , Suman Ghosh This is my paper

Pith reviewed 2026-05-23 17:18 UTC · model grok-4.3

classification 🌀 gr-qc
keywords gravitational lensingdeflection angleEllis-Bronnikov wormholebraneworldnull geodesicsphoton sphereEinstein ringwormhole throat
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The pith

The steepness parameter m in generalized Ellis-Bronnikov wormholes produces distinct signatures in deflection angles, Einstein ring radii, and image positions, while warped extra dimensions broaden the photon sphere.

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

This paper calculates null geodesic paths and gravitational lensing for generalized Ellis-Bronnikov wormholes that extend the standard Ellis-Bronnikov geometry through a steepness parameter m greater than or equal to 2. Analytic expressions for the deflection angle are derived in weak and strong regimes, recovering the known results at m equals 2, with approximations and numerics applied for larger m. The analysis demonstrates that m generates measurable differences in deflection angles, ring radii, and image locations. Embedding the geometry in a five-dimensional warped braneworld introduces an extra-dimensional momentum parameter that changes the effective impact parameter and widens the photon sphere along with the lensed images.

Core claim

In the generalized Ellis-Bronnikov wormhole spacetime controlled by the steepness parameter m, the deflection angle depends on m and yields distinct Einstein ring radii and image positions; the warped five-dimensional braneworld embedding encodes extra-dimensional effects through the parameter delta associated with photon momentum along the extra dimension, which modifies the effective impact parameter and produces a broadened photon sphere and lensed images.

What carries the argument

Null geodesic integration in the generalized Ellis-Bronnikov metric with throat shape controlled by steepness parameter m, extended to a warped braneworld background via the extra-dimensional momentum parameter delta.

Load-bearing premise

The generalized Ellis-Bronnikov metric and its warped braneworld embedding are the correct spacetime geometries for integrating the null geodesic equation to obtain light deflection and lensing quantities.

What would settle it

A measurement of deflection angle or Einstein ring radius around a wormhole candidate that shows no variation with the steepness parameter m or the extra-dimensional parameter delta would contradict the claimed signatures.

Figures

Figures reproduced from arXiv: 2411.10804 by Soumya Jana, Suman Ghosh, Vivek Sharma.

Figure 1
Figure 1. Figure 1: FIG. 1. Plot of deflection angles of photon trajectories in 4-D and 5-D models. Each panel [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Schematic diagram of gravitational lensing by a point source. [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
read the original abstract

We investigate null trajectories, deflection angles, and gravitational lensing in the spacetime of generalized Ellis-Bronnikov (GEB) wormholes and their embedding in a five-dimensional warped braneworld background (WGEB). The GEB geometry extends the standard Ellis-Bronnikov (EB) wormhole by introducing a steepness parameter $m \geq 2$, which controls the shape of the wormhole throat while partially improving on the violation of classical energy conditions. We compare the lensing properties of the four-dimensional GEB geometry with those of its warped five-dimensional counterpart, where the effect of the extra dimension is encoded through the parameter $\delta$, associated with the photon momentum along the extra dimension. Analytic expressions for the deflection angle are obtained in both weak and strong-lensing regimes, and the known EB results are recovered for $m = 2$. For $m > 2$, analytic approximation and numerical analysis is used where exact analytic solutions are not available. We show that the parameter $m$ leaves clear and distinguishable signatures in the deflection angle, Einstein ring radius, and image positions, while the presence of the warped extra dimension modifies the effective impact parameter and leads to a broadening of the photon sphere and lensed images.

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 / 3 minor

Summary. The manuscript investigates null geodesics, deflection angles, and gravitational lensing for generalized Ellis-Bronnikov (GEB) wormholes with shape-function steepness m ≥ 2 and their five-dimensional warped braneworld embeddings (WGEB) parameterized by δ. Analytic expressions for the deflection angle are derived in the weak-field limit and for the strong-lensing regime where possible; numerical integration is employed for m > 2. The m = 2 Ellis-Bronnikov limit is recovered. The central claim is that m produces distinguishable signatures in the deflection angle, Einstein-ring radius, and image positions, while δ modifies the effective impact parameter and broadens the photon sphere and lensed images.

Significance. If the derivations hold, the work supplies concrete, parameter-dependent predictions for lensing observables around these wormhole geometries, extending prior Ellis-Bronnikov results with both analytic closed forms and numerical results for m > 2. Explicit recovery of the known m = 2 limit provides a built-in validation check. The inclusion of the warped extra dimension via δ offers a controlled way to explore higher-dimensional effects on photon trajectories.

major comments (1)
  1. The abstract states that 'analytic expressions for the deflection angle are obtained in both weak and strong-lensing regimes' yet notes that 'for m > 2, analytic approximation and numerical analysis is used where exact analytic solutions are not available.' The manuscript should clarify in §3 or §4 which strong-lensing quantities remain fully analytic versus those requiring the numerical integration of the null geodesic equation, and whether the reported Einstein-ring radii for m > 2 are obtained from the analytic approximation or the numerical solution.
minor comments (3)
  1. The abstract provides no information on the numerical integrator, step-size control, or convergence tests used for the strong-field deflection angles when m > 2. Adding a brief statement on these checks would strengthen the numerical results.
  2. Notation for the effective impact parameter in the WGEB case (including the δ term) should be introduced explicitly in the text before its first use in the deflection-angle formulas, rather than appearing only in the final expressions.
  3. Figure captions for the lensing images or deflection-angle plots should state the specific values of m and δ employed, and whether the curves correspond to the analytic or numerical branch.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment and the specific suggestion for improving clarity. We address the single major comment below.

read point-by-point responses

  1. Referee: The abstract states that 'analytic expressions for the deflection angle are obtained in both weak and strong-lensing regimes' yet notes that 'for m > 2, analytic approximation and numerical analysis is used where exact analytic solutions are not available.' The manuscript should clarify in §3 or §4 which strong-lensing quantities remain fully analytic versus those requiring the numerical integration of the null geodesic equation, and whether the reported Einstein-ring radii for m > 2 are obtained from the analytic approximation or the numerical solution.

    Authors: We agree that the distinction between analytic and numerical results for m > 2 in the strong-lensing regime could be stated more explicitly. In the revised version we will add a short clarifying paragraph at the beginning of §4 (Strong lensing) stating: (i) the deflection angle and critical impact parameter for the m = 2 case remain fully analytic; (ii) for m > 2 the exact integral for the deflection angle has no closed form and is evaluated numerically via the null geodesic equation; (iii) the Einstein-ring radii and image positions reported for m > 2 are obtained from this numerical integration (with the analytic weak-field approximation used only for cross-checks at large impact parameters). The abstract will be left unchanged because it already flags the use of numerical methods for m > 2, but the new paragraph will remove any ambiguity. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper specifies the GEB metric ansatz (with shape-function steepness m) and its WGEB embedding (with extra-dimension parameter δ), then computes deflection angles, Einstein-ring radii, and image positions via direct integration or approximation of the null geodesic equation. Known EB results are recovered for m=2 as a consistency check, and numerical trends are reported for m>2. These outputs are derived quantities from the supplied metrics; they do not reduce by the paper's own equations to fitted parameters renamed as predictions, nor to any self-citation chain. The reader's assessment of score 1.0 is consistent with this self-contained derivation.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on the assumed validity of the GEB and WGEB metric ansatze together with the standard treatment of photons as null geodesics; m and δ function as free model parameters rather than fitted constants.

free parameters (2)
  • m
    Steepness parameter that controls throat shape and is introduced to generalize the Ellis-Bronnikov wormhole.
  • δ
    Parameter encoding photon momentum along the extra dimension in the warped braneworld embedding.
axioms (2)
  • standard math Light follows null geodesics in the given spacetime metric.
    Standard assumption in general relativity for photon trajectories.
  • domain assumption The provided metric forms for GEB and WGEB correctly describe the background geometry.
    The calculations presuppose these metric ansatze without independent derivation.
invented entities (1)
  • Generalized Ellis-Bronnikov wormhole no independent evidence
    purpose: Model spacetime connecting distant regions with tunable throat shape.
    Hypothetical construct introduced to study traversable wormholes; no independent observational evidence is supplied.

pith-pipeline@v0.9.0 · 5761 in / 1421 out tokens · 43325 ms · 2026-05-23T17:18:22.543743+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • Foundation/AlexanderDuality.lean alexander_duality_circle_linking contradicts
    ?
    contradicts

    CONTRADICTS: the theorem conflicts with this paper passage, or marks a claim that would need revision before publication.

    the general form of the 4D-line-element embedded in a warped 5D spacetime is ds² = g_μν dx^μ dx^ν + g_44 (dx⁴)² ... y is the extra dimension (−∞≤y≤∞)

  • Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction contradicts
    ?
    contradicts

    CONTRADICTS: the theorem conflicts with this paper passage, or marks a claim that would need revision before publication.

    Metric (2.3) is spherically symmetric ... r(l) = (b₀^m + l^m)^{1/m} ... 5D-WGEB wormhole

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The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
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unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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