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arxiv: 2503.09222 · v1 · pith:IBLKHVUCnew · submitted 2025-03-12 · 🌀 gr-qc · math-ph· math.MP

Energy Conditions and Stability of Charged Wormholes in f(R, mathscr{L}_m) Gravity: A Comparative Analysis with Compact Objects

Sagar V. Soni , A. C. Khunt , Farook Rahaman , A.H. Hasmani This is my paper

Pith reviewed 2026-05-23 00:10 UTC · model grok-4.3

classification 🌀 gr-qc math-phmath.MP
keywords energychargechargedconditionsgravitymathcalstabilitywormholes
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The pith

Charged wormholes in f(R, L_m) gravity satisfy radial null energy condition over wide charge ranges but tangential condition only for 0.1 to 0.6, enabling stable throat structures.

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

The paper investigates energy conditions for charged traversable wormholes in f(R, L_m) modified gravity. Using the Exponential Spheroid shape function model and two choices of charge function, it derives expressions for energy density and radial and tangential pressures. The radial null energy condition holds across a broad range of charge parameters E consistent with physical laws, while the tangential null energy condition holds only for 0.1 ≤ E ≤ 0.6, with violations at higher values indicating the throat-like structure needed for stability. Pressure-density profiles are compared to those of neutron stars and show distinct matter distributions.

Core claim

Our findings show that the radial NEC remains satisfied across a wide range of charge parameters E consistent with established physical laws. However, the tangential NEC is only sustained in the range 0.1 ≤ E ≤ 0.6; for higher charge values, violations occur, indicating the formation of a throat-like structure necessary for wormhole stability. Additionally, we compare the pressure-density profiles of these charged wormholes with those of compact objects such as neutron stars, revealing distinct variations in matter distribution.

What carries the argument

The Exponential Spheroid shape function together with two explicit forms of the charge function E^2, used to obtain energy density and pressure expressions and test the null energy conditions in the f(R, L_m) framework.

If this is right

  • Radial null energy condition holds for many physically allowed charge values.
  • Tangential null energy condition restricts to the interval 0.1 to 0.6.
  • Violations of the tangential condition at higher charge values signal the throat structure required for stability.
  • Pressure-density profiles differ from those of neutron stars, indicating distinct matter distributions.
  • Charge parameter and the modified gravity framework together control wormhole stability characteristics.

Where Pith is reading between the lines

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

  • Charge values could be tuned to produce stable wormhole solutions within this class of modified gravity theories.
  • The distinction in matter profiles from neutron stars suggests possible observational signatures that separate wormholes from compact stars.
  • Similar charge-dependent behavior might appear when the same analysis is repeated in other modified gravity models.
  • The qualitative role of charge in controlling throat formation may survive changes to the shape function.
  • wormholes
  • energy conditions
  • modified gravity
  • null energy condition

Load-bearing premise

The reported ranges for satisfaction of the null energy conditions rest on the specific Exponential Spheroid shape function, the chosen forms of E^2, and one fixed but unspecified version of f(R, L_m); altering any of these modeling choices would shift the ranges.

What would settle it

Explicit computation of the tangential null energy condition for the Exponential Spheroid model at charge value E=0.7, checking whether it is violated as predicted while the radial condition remains satisfied.

Figures

Figures reproduced from arXiv: 2503.09222 by A. C. Khunt, A.H. Hasmani, Farook Rahaman, Sagar V. Soni.

Figure 1
Figure 1. Figure 1: Density ρ plotted against the radial r for the ES-model The density profile which was computed using Eq. (22) is shown in [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Nature of b(r), throat condition b(r) < r, flaring-out condition b ′ (r) < 1, and asymptotic flatness limr→∞ b(r) r = 0 for r0 = 0.9, A = 0.5, ρ0 = 0.07, and α = {2.5, 3.0, 3.5}. The radial pressure and tangential pressure can be expressed as pr = 1 α " (α − 1)ρ0e −r + αA + e −r α3r 3 [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Left: Radial pressure pr and Right: Tangential pressure pt against the radius r for the ES model. The graph shows different curve for the values of α for 2.5, 3.0, and 3.5, with the model parameter set to A = 0.5, the density parameter ρ0 = 0.07 and r0 = 0.9 for the charge function E 2 = A. seen in [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Nature of b(r), throat condition b(r) < r, flaring-out condition b ′ (r) < 1, and asymptotic flatness limr→∞ b(r) r = 0 for r0 = 0.9, ρ0 = 0.07, and α = {2.5, 3.0, 3.5}. 13 [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Left: Radial pressure pr and Right: Tangential pressure pt against the radius r for the ES model. The graph shows different curve for the values of α for 2.5, 3.0, and 3.5., the density parameter ρ0 = 0.07 and r0 = 0.9 for the charge function E 2 = r 2 . necessities. However, the anisotropic stress distribution supports the general stability of the wormhole structure. Figs. 6 show the anisotropy profile ∆ … view at source ↗
Figure 6
Figure 6. Figure 6: (a) Radial variation of anisotropy parameter ∆ for the SF- [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Density ρ plotted against the radius r for a charged wormhole. The plot shows different curves for electric charge values E ranging from 0 to 1, with the model parameters set to α = 0.5, EoS parameter ω = 2.5, and throat radius r0 = 1 [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) Radial pressure pr and (b) tangential pressure pt plotted against the radius r for a charged wormhole. The graphs show different curves for electric charge values E ranging from 0 to 1, with the model parameters set to α = 0.5, EoS parameter ω = 2.5, and throat radius r0 = 1. The profile for the pr shows positive values across the whole range that is taken into consideration, including the exterior reg… view at source ↗
Figure 9
Figure 9. Figure 9: Radial variation of anisotropy parameter ∆ for [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Left: Radial NEC and Right: Tangential NEC for SF-I [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Left: Radial NEC and Right: Tangential NEC for SF-II We present the NEC for the ES density model, taking into consideration two distinct charge function choices, for both the NECr and NECt compo￾nents. The NEC is shown for the charge function E 2 = A in [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Null energy condition (NEC) for radial and tangential pressures for different [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
read the original abstract

In this paper, we study the energy conditions of charged traversable wormholes in the framework of $f(R, \mathscr{L}_m)$ modified gravity. In the first case, we derive the shape functions (SFs) for two different choices of the charge function $\mathcal{E}^2$ by considering the Exponential Spheroid (ES) model and analyze the null energy condition (NEC). In the second case, we consider a particular shape function and study its implications for the energy conditions. In both cases, we obtain expressions for energy density and pressure in radial and tangential directions. Our findings show that the radial NEC remains satisfied across a wide range of charge parameters $\mathcal{E}$ consistent with established physical laws. However, the tangential NEC is only sustained in the range $0.1 \leq \mathcal{E} \leq 0.6$; for higher charge values, violations occur, indicating the formation of a throat-like structure necessary for wormhole stability. Additionally, we compare the pressure-density profiles of these charged wormholes with those of compact objects such as neutron stars, revealing distinct variations in matter distribution. This analysis highlights the crucial role of charge and modified gravity in determining the stability and physical characteristics of wormhole structures.

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 / 0 minor

Summary. The paper studies energy conditions of charged traversable wormholes in f(R, ℒ_m) gravity. In the first case, shape functions are derived for two choices of charge function ℰ² using the Exponential Spheroid model and null energy conditions (NEC) are analyzed. In the second case, a particular shape function is considered. Expressions for energy density and radial/tangential pressures are obtained. The central claim is that radial NEC holds across a wide range of charge parameter ℰ consistent with physical laws, while tangential NEC holds only for 0.1 ≤ ℰ ≤ 0.6; violations at higher ℰ indicate throat-like structure for stability. Pressure-density profiles are compared to those of compact objects such as neutron stars.

Significance. If the results hold, the work illustrates how the charge parameter and modified gravity affect the satisfaction of energy conditions in wormhole spacetimes and provides a comparison of matter profiles with those of neutron stars, potentially aiding in distinguishing wormhole candidates from compact objects.

major comments (3)
  1. [Abstract] Abstract: the headline result that tangential NEC holds only for 0.1 ≤ ℰ ≤ 0.6 (with violations at higher values indicating throat structure) is obtained by direct substitution of the Exponential Spheroid shape function and the two chosen ℰ² forms into the modified field equations; the paper provides no demonstration that this specific interval survives for other shape functions obeying the flaring-out conditions b(r₀)=r₀, b'(r₀)<1 and b(r)/r→0 at infinity.
  2. The analysis depends on a fixed but unspecified form of f(R, ℒ_m); the signs of the NEC combinations (ρ + p_r and ρ + p_t) are outputs of this choice together with the ES model, and no variation of the functional form is performed to test whether the reported ℰ ranges are structural or model-dependent.
  3. The second case with a particular (fixed) shape function is mentioned but no explicit comparison is given showing whether the 0.1–0.6 interval for tangential NEC persists or changes, leaving the generality of the central claim untested.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment point by point below, indicating where revisions will be made to improve clarity and address concerns about specificity and generality.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline result that tangential NEC holds only for 0.1 ≤ ℰ ≤ 0.6 (with violations at higher values indicating throat structure) is obtained by direct substitution of the Exponential Spheroid shape function and the two chosen ℰ² forms into the modified field equations; the paper provides no demonstration that this specific interval survives for other shape functions obeying the flaring-out conditions b(r₀)=r₀, b'(r₀)<1 and b(r)/r→0 at infinity.

    Authors: We agree that the reported range for tangential NEC is obtained specifically within the Exponential Spheroid model (first case, with two charge functions) and the particular shape function (second case). The manuscript does not claim or demonstrate that this interval holds for arbitrary shape functions satisfying the flaring-out conditions. We will revise the abstract to explicitly state that the findings apply to the models considered and add a clarifying remark in the discussion section on the model-specific nature of the results, noting that broader exploration of other shape functions is left for future work. revision: yes

  2. Referee: The analysis depends on a fixed but unspecified form of f(R, ℒ_m); the signs of the NEC combinations (ρ + p_r and ρ + p_t) are outputs of this choice together with the ES model, and no variation of the functional form is performed to test whether the reported ℰ ranges are structural or model-dependent.

    Authors: The specific functional form of f(R, ℒ_m) employed is defined in the manuscript; we will make this explicit and prominent in the revised version to avoid any ambiguity. Our analysis is performed within this fixed choice of the theory to obtain the energy conditions and compare with compact objects. We concur that no variation over alternative functional forms was conducted, as that would constitute a separate study. We will add a brief note in the conclusions acknowledging this model dependence and the potential for future investigations into other forms. revision: partial

  3. Referee: The second case with a particular (fixed) shape function is mentioned but no explicit comparison is given showing whether the 0.1–0.6 interval for tangential NEC persists or changes, leaving the generality of the central claim untested.

    Authors: The second case is presented to study the implications of an alternative shape function on the energy density and pressure profiles. While the expressions are derived, we did not provide a direct numerical comparison of the tangential NEC range. We will revise the manuscript to include an explicit comparison between the two cases, indicating whether and how the 0.1–0.6 interval changes or persists under the particular shape function. revision: yes

Circularity Check

0 steps flagged

No circularity: explicit model-dependent NEC evaluation

full rationale

The paper substitutes chosen Exponential Spheroid shape functions and two explicit E^2(r) forms into the modified field equations, then computes the resulting ρ, p_r, p_t and checks the sign of the NEC combinations for different numerical values of the charge parameter E. The quoted interval 0.1 ≤ E ≤ 0.6 is the direct numerical output of that substitution for the adopted ansätze; it is not obtained by fitting E to a subset of data and then relabeling the fit as a prediction, nor does any step reduce to a self-citation or self-definition. The second case (fixed shape function) is likewise an explicit calculation. Because the derivation chain consists of algebraic substitution followed by inequality checks on the output expressions, the reported ranges are model-specific results rather than tautological restatements of the inputs. No load-bearing uniqueness theorem or ansatz smuggling is invoked.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on two modeling choices (Exponential Spheroid shape function and two explicit E^2 forms) plus an unspecified f(R, L_m) that are introduced without independent justification or external calibration.

free parameters (1)
  • charge parameter E
    The interval 0.1 ≤ E ≤ 0.6 is obtained by direct substitution into the NEC expressions; the bounds are therefore fitted to the chosen metric ansatz.
axioms (2)
  • domain assumption The wormhole metric is static and spherically symmetric with the given shape function and charge function forms.
    Invoked at the start of the derivation of energy density and pressures.
  • domain assumption The modified gravity function f(R, L_m) admits the standard field equations used to obtain the stress-energy components.
    Required to translate the metric into energy density and pressures.

pith-pipeline@v0.9.0 · 5783 in / 1491 out tokens · 61058 ms · 2026-05-23T00:10:52.104758+00:00 · methodology

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