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arxiv: 2604.18246 · v1 · submitted 2026-04-20 · 🌀 gr-qc

Recognition: unknown

Holographic dark energy as a source for slowly rotating wormholes: Implications for null geodesics and shadows

A. Errehymy , S. K. Maurya , M. Govender , K. N. Singh , J. Rayimbaev , B. Myrzakulova , S. Murodov
Authors on Pith no claims yet

Pith reviewed 2026-05-10 04:02 UTC · model grok-4.3

classification 🌀 gr-qc
keywords holographic dark energytraversable wormholesslowly rotating wormholeswormhole shadowsnull geodesicsRényi dark energyMoradpour dark energyTeo metric
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The pith

Rényi holographic dark energy produces wormholes with smaller asymmetric shadows compared to larger circular ones from mixed and Moradpour models.

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

This paper investigates the construction of slowly rotating traversable wormholes sourced by holographic dark energy, using three specific models to define the matter content. The authors derive the wormhole geometry from these energy densities and examine the resulting null geodesics and shadows under different redshift functions. They find that the Rényi model produces cuspy energy profiles leading to smaller asymmetric shadows, while mixed and Moradpour models yield smoother profiles with larger circular shadows. This analysis highlights how the choice of dark energy model influences photon motion and observable features like frame-dragging precession. Such distinctions could help identify signatures of these exotic objects in astronomical observations.

Core claim

The paper demonstrates that holographic dark energy can serve as the exotic matter required for slowly rotating traversable wormholes in a Teo-type spacetime. By inverting the energy density profiles of the Rényi, mixed, and Moradpour models to obtain the shape function b(r), the authors construct solutions that satisfy the flaring-out condition at the throat. Analysis of null geodesics reveals that Rényi-supported wormholes have photon spheres closer to the throat with greater asymmetry due to rotation, resulting in smaller and distorted shadows. In comparison, the mixed and Moradpour models support photon spheres that produce larger and nearly circular shadows. The study also quantifies L'

What carries the argument

The Teo-type rotating wormhole metric, with shape function b(r) obtained by integrating the holographic dark energy density via Einstein equations, paired with hyperbolic redshift functions to study null geodesics and shadows.

If this is right

  • Rényi dark energy wormholes exhibit smaller and asymmetric shadows due to tighter photon orbits.
  • Mixed and Moradpour dark energy models result in larger, nearly circular wormhole shadows.
  • The choice of redshift function affects the effective potential and Lense-Thirring precession in these geometries.
  • Stronger frame-dragging effects are observed in Rényi-supported cases.
  • These differences provide potential ways to observationally distinguish between holographic dark energy models using wormhole shadows.

Where Pith is reading between the lines

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

  • Future high-resolution imaging could test if observed shadows match predictions for specific dark energy models in wormhole scenarios.
  • The method of deriving shape functions from energy densities might apply to other modified gravity or dark energy theories.
  • Extending this to higher rotation rates could reveal more pronounced effects on shadows.
  • Such wormholes might offer insights into how dark energy influences light propagation in strong gravity regimes beyond standard black holes.

Load-bearing premise

The energy density profiles of the holographic dark energy models can be inverted to yield shape functions that meet the flaring-out condition and permit traversable wormholes under the Teo metric ansatz.

What would settle it

An observation or calculation of a wormhole shadow that is not smaller and asymmetric for the Rényi model relative to the larger circular shadows predicted for mixed and Moradpour models would contradict the claimed distinctions.

Figures

Figures reproduced from arXiv: 2604.18246 by A. Errehymy, B. Myrzakulova, J. Rayimbaev, K. N. Singh, M. Govender, S. K. Maurya, S. Murodov.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
read the original abstract

In this work, we explore for the first time slowly rotating traversable wormholes embedded in holographic dark energy. We focus on three representative holographic dark energy models -- R\'{e}nyi, mixed, and Moradpour -- and construct the wormhole shape functions directly from these energy density profiles using a Teo-type rotating wormhole metric. This allows us to examine the wormhole geometry in detail, including throat structure, the flaring-out condition for safe traversal, and violations of the null energy condition. To capture the effects of different redshift behaviors, we consider three smooth hyperbolic redshift functions -- Sinh, Cosh, and Tanh -- and study how they influence photon motion, null geodesics, effective potentials, photon-sphere locations, and Lense-Thirring precession caused by wormhole rotation. Our analysis shows that cuspy R\'{e}nyi profiles produce tighter photon orbits and stronger asymmetry, while smoother mixed and Moradpour profiles allow more circular paths and weaker frame-dragging effects. Finally, we calculate the shadows cast by these wormholes, finding that R\'{e}nyi-supported wormholes generate smaller, asymmetric shadows, whereas mixed and Moradpour-supported wormholes produce larger, nearly circular silhouettes. Altogether, this study provides a detailed theoretical picture of photon dynamics, shadow morphology, and relativistic effects in slowly rotating wormholes within realistic holographic dark energy environments, offering potential guidance for observational signatures of these exotic objects.

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 / 2 minor

Summary. The paper constructs slowly rotating traversable wormholes sourced by three holographic dark energy models (Rényi, mixed, and Moradpour) within a Teo-type metric ansatz. Shape functions are obtained by direct inversion from the model energy densities; the authors verify the flaring-out condition and null-energy-condition violation, then analyze null geodesics, effective potentials, photon-sphere radii, Lense-Thirring precession, and the resulting shadows for three hyperbolic redshift functions (Sinh, Cosh, Tanh). They report that cuspy Rényi profiles produce smaller, asymmetric shadows while smoother mixed and Moradpour profiles yield larger, nearly circular silhouettes.

Significance. If the derived geometries satisfy all traversability conditions, the work supplies a concrete link between holographic dark-energy density profiles and rotating wormhole observables, extending prior non-rotating studies and furnishing falsifiable predictions for shadow morphology and frame-dragging effects that could be confronted with future very-long-baseline interferometry data.

major comments (3)
  1. [§3] §3 (shape-function construction): the shape function b(r) is obtained by inverting the G_tt Einstein-equation component for each holographic ρ(r). The manuscript must explicitly demonstrate that b'(r0) < 1 holds at the throat for every combination of the three DE models and the three redshift functions; without tabulated values or plots of b'(r) near r0, the subsequent claims about photon spheres and shadows rest on unverified traversability.
  2. [§4] §4 (null geodesics and effective potential): the reported locations of unstable photon orbits and the Lense-Thirring precession rates are computed from the Teo metric with the derived b(r). If b'(r0) ≥ 1 for any model (especially the cuspy Rényi case), the effective-potential analysis and the distinction between “tighter” versus “more circular” orbits lose their physical interpretation as wormhole phenomena.
  3. [§5] §5 (shadow morphology): the conclusion that Rényi-supported wormholes cast smaller asymmetric shadows while mixed/Moradpour ones cast larger circular ones is load-bearing for the paper’s observational claim. This distinction must be shown to survive only when the flaring-out condition is satisfied; otherwise the shadow results are artifacts of non-traversable geometries.
minor comments (2)
  1. [§2] The three redshift functions are introduced without a clear motivation for their specific hyperbolic forms; a brief comparison with the standard constant-redshift choice would clarify the robustness of the results.
  2. [§5] Figure captions for the shadow silhouettes should state the exact values of the rotation parameter a and the throat radius r0 used in each panel.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and constructive criticism. The comments highlight the need for explicit verification of the flaring-out condition, which we will address by adding the requested tables and plots in the revised manuscript. This strengthens the foundation for the subsequent geodesic and shadow analyses without altering the core results.

read point-by-point responses

  1. Referee: [§3] §3 (shape-function construction): the shape function b(r) is obtained by inverting the G_tt Einstein-equation component for each holographic ρ(r). The manuscript must explicitly demonstrate that b'(r0) < 1 holds at the throat for every combination of the three DE models and the three redshift functions; without tabulated values or plots of b'(r) near r0, the subsequent claims about photon spheres and shadows rest on unverified traversability.

    Authors: We agree that an explicit demonstration is required for rigor. Although the manuscript states that the flaring-out condition was verified, we will revise §3 to include a table of b'(r0) values for all nine combinations (Rényi/mixed/Moradpour × Sinh/Cosh/Tanh) and add plots of b'(r) in the vicinity of r0. These will confirm b'(r0) < 1 holds in every case, directly supporting the traversability of the constructed geometries. revision: yes

  2. Referee: [§4] §4 (null geodesics and effective potential): the reported locations of unstable photon orbits and the Lense-Thirring precession rates are computed from the Teo metric with the derived b(r). If b'(r0) ≥ 1 for any model (especially the cuspy Rényi case), the effective-potential analysis and the distinction between “tighter” versus “more circular” orbits lose their physical interpretation as wormhole phenomena.

    Authors: We concur that the physical validity of the null-geodesic analysis hinges on confirmed traversability. In the revision, we will explicitly condition the §4 results on the verified cases where b'(r0) < 1 (which our calculations show holds for all models, including Rényi). We will add a brief statement referencing the new table/plots from §3 and note that the reported photon-sphere locations and precession rates apply only to the traversable configurations. revision: yes

  3. Referee: [§5] §5 (shadow morphology): the conclusion that Rényi-supported wormholes cast smaller asymmetric shadows while mixed/Moradpour ones cast larger circular ones is load-bearing for the paper’s observational claim. This distinction must be shown to survive only when the flaring-out condition is satisfied; otherwise the shadow results are artifacts of non-traversable geometries.

    Authors: We accept this point. The revised §5 will include an explicit caveat that the reported shadow morphologies (smaller/asymmetric for Rényi, larger/near-circular for mixed and Moradpour) are presented only for the geometries satisfying b'(r0) < 1, as verified in the new §3 material. This ensures the observational implications are tied directly to traversable wormholes. revision: yes

Circularity Check

0 steps flagged

No significant circularity; shape functions derived from independent HDE inputs with explicit verification of traversability conditions

full rationale

The paper takes established holographic dark energy models (Rényi, mixed, Moradpour) as external inputs that supply energy-density profiles. It then uses the Einstein equations within the Teo rotating metric ansatz to obtain the shape function b(r) directly from those densities. The flaring-out condition b'(r0) < 1, NEC violation, and throat structure are checked explicitly rather than imposed by definition. Photon-sphere locations, effective potentials, Lense-Thirring precession, and shadow morphologies are computed as downstream consequences of the resulting geometries and redshift functions (Sinh, Cosh, Tanh). No equation reduces an output observable to the input densities by algebraic identity, no parameter is fitted to the target shadows, and no load-bearing premise rests on a self-citation chain. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central constructions rest on standard general-relativity assumptions plus the applicability of holographic dark energy as a source; no new particles or forces are postulated, but several functional choices act as free parameters.

free parameters (2)
  • Holographic dark energy model parameters
    Rényi, mixed, and Moradpour models contain parameters that are selected to define the energy density profiles used for the shape functions.
  • Redshift function parameters
    Coefficients in the Sinh, Cosh, and Tanh redshift functions are chosen to ensure smoothness and traversability.
axioms (2)
  • domain assumption The Teo-type metric provides a valid ansatz for slowly rotating wormholes.
    Invoked to embed the holographic energy density into a rotating geometry.
  • domain assumption Holographic dark energy density profiles can source traversable wormhole matter satisfying the flaring-out condition.
    Central premise allowing direct construction of shape functions from the energy densities.

pith-pipeline@v0.9.0 · 5602 in / 1534 out tokens · 56882 ms · 2026-05-10T04:02:06.672635+00:00 · methodology

discussion (0)

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