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arxiv: 2510.23689 · v1 · submitted 2025-10-27 · 🌀 gr-qc

Thin-shell wormhole with a background Kalb-Ramond Field

Arya Dutta , Farook Rahaman This is my paper

Pith reviewed 2026-05-18 03:24 UTC · model grok-4.3

classification 🌀 gr-qc
keywords thin-shell wormholeKalb-Ramond fieldenergy conditionslinear stabilityLorentz violationcut-and-paste constructionexotic mattermodified black hole
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The pith

Thin-shell wormholes from Kalb-Ramond modified black holes violate the null and weak energy conditions but satisfy the strong energy condition and are linearly stable.

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

The paper constructs a thin-shell wormhole by cutting and pasting two copies of a black hole metric modified by a non-minimal Kalb-Ramond field coupling. It calculates the surface matter properties on the throat and finds violations of the null and weak energy conditions alongside satisfaction of the strong energy condition. The throat radius is shown to have a specific time-dependent velocity, and the setup proves linearly stable to small radial perturbations. A reader might care because this offers an explicit example of a potentially traversable wormhole in a Lorentz-violating spacetime motivated by string theory.

Core claim

Considering two copies of the modified black hole solution arising from the non-minimal coupling between the Kalb-Ramond vacuum expectation value and the Ricci tensor, the cut-and-paste construction yields a thin-shell wormhole whose surface stress-energy tensor violates the null and weak energy conditions but obeys the strong energy condition. The dynamics of the throat radius are derived from the Israel junction conditions, yielding a determined velocity, and linear stability analysis confirms stability against small radial perturbations for appropriate parameter ranges.

What carries the argument

The cut-and-paste thin-shell construction using the Israel junction conditions applied to the modified black hole metric with non-minimal Kalb-Ramond coupling to the Ricci tensor.

If this is right

  • The total amount of exotic matter at the throat changes with the Lorentz-violating parameters.
  • The equation of state and pressure-density relation for the shell matter are fixed by the junction conditions.
  • Test particle geodesics near the throat follow paths determined by the background metric and parameters.
  • The throat radius evolves according to a specific velocity derived from the shell dynamics.

Where Pith is reading between the lines

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

  • The stability result could be tested by examining whether the same construction remains stable when the background metric is replaced by other Lorentz-violating solutions.
  • Tidal forces experienced by an observer crossing the throat might be computed to assess practical traversability.
  • The parameter dependence of the exotic matter could connect to constraints from cosmological observations of Lorentz violation.

Load-bearing premise

A modified black hole solution exists that arises from the non-minimal coupling of the Kalb-Ramond vacuum expectation value to the Ricci tensor and can be used as the background metric for the cut-and-paste construction.

What would settle it

A direct computation of the surface stress-energy tensor showing that the null energy condition holds for all values of the Lorentz-violating parameters would falsify the reported violation.

Figures

Figures reproduced from arXiv: 2510.23689 by Arya Dutta, Farook Rahaman.

Figure 1
Figure 1. Figure 1: The variation in the metric function f(r) with the radial coordinate r is shown. We have taken three sets of values for the LV parameters γ and λ (which meet our given constraints) and plotted f(r) (solid lines) for five different masses (M varies from 109 to 5.109 Kg) in each of these three cases. The dashed lines represent Schwarzschild Black Holes corresponding to each M, γ, and λ. Note that the r-inter… view at source ↗
Figure 2
Figure 2. Figure 2: The variation of the energy density σ with the throat radius a(km), for different masses and LV parameters. We choose typical wormholes whose radii fall within the range of 1 to 10 km. Since σ < 0 from these plots, the first condition for the Weak Energy Condition (WEC) is violated [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The variation of the thermodynamic pressure [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The variation of the σ + p with the throat radius a(km). In all three cases, (σ + p) < 0; i.e., NEC is violated. This picture also provides the second condition for the violation of WEC. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The variation of the σ + 3p with the throat radius a(km). The plots show that (σ + 3p) > 0; i.e., the wormhole satisfies the Strong Energy Condition. 4 Equation of State (EOS) Let the EoS at the surface Σ be p = ωσ, ω ≡ constant. From Eqs. 3 and 3, the EOS parameter ω can be written as ω = p σ = − 1 2 − 1 2 . GM a − 1 λ . γ a 2/λ 1 − 2GM a + γ a 2/λ . (15) [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The variation of the EOS parameter ω = (p/σ) with the throat radius a(km). A close observation reveals that −1 < ω < − 1 3 , so the shell is supported by dark-energy￾like matter. this equation, we find that g(a) ≡ 2 − 3GM a + (2 − 1 λ ) γ a 2/λ = 0. (16) (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The variation of the function g(a) with the throat radius a(km). For reference, f(a) for each case is also shown with the dashed lines. Clearly, r+ (outer radius) for each g(a) (solid lines) is less than the corresponding r+ for f(a). Plotting g(a) in [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The variation of the α(r) with the throat radius r, for various masses and LV parameters. r0 is the point where α(r) cuts the r curve. Each curve has a different intersection point; we have pointed out the general expression of the intersecting points. In general, a wormhole is attractive for a r > 0 and repulsive for a r < 0. The Eq. 20 and the [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The nature of the velocity of the radius of the throat at time [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The Variation of the total exotic matter at the shell [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The variation of the total exotic matter at the shell [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The variation of β 2 with a0, for various masses and LV parameters. These plots indicate the stability regions of the corresponding wormholes. We have plotted β 2 with respect to a0 in [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
read the original abstract

The Kalb-Ramond field is a background tensor field that arises in string theory and violates local Lorentz symmetry of spacetime, upon acquiring the Vacuum Expectation Value. A non-minimal coupling between the Kalb-Ramond VEV and the Ricci tensor may give rise to a modified black hole solution. Considering two copies of such black holes, we construct a thin-shell wormhole using the Cut-and-Paste technique. Then we investigate key physical properties of the wormhole like pressure-density profile, equation of state, the geodesic motion of test particles near the wormhole throat, and the total amount of exotic matter in the throat, and examine how these properties vary with the Lorentz-Violating parameters. We find that the wormhole model violates the null and weak energy conditions, but satisfies the strong energy condition. On top of that, the velocity of the throat radius is found considering its time evolution. Finally, we analyze its linear stability against small radial perturbations.

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 a thin-shell wormhole by the cut-and-paste method on two copies of a modified black-hole metric asserted to arise from non-minimal coupling of a Kalb-Ramond vacuum expectation value to the Ricci tensor. It computes the surface stress-energy tensor, examines the equation of state and energy conditions (finding violation of NEC and WEC but satisfaction of SEC), studies geodesic motion and the total exotic matter, derives the time evolution of the throat radius, and performs a linear stability analysis against radial perturbations, all as functions of the Lorentz-violating parameters.

Significance. If the background metric is shown to be a consistent solution of the modified field equations, the work would supply a concrete example of a traversable thin-shell wormhole in a Lorentz-violating string-inspired background, with explicit dependence of stability and energy-condition violation on the Lorentz-violating parameters. The parameter study and the explicit velocity and stability calculations are potentially useful additions to the thin-shell wormhole literature.

major comments (3)
  1. [§2] §2 (or equivalent): The modified black-hole metric f(r; ℓ) is introduced without an explicit derivation from the non-minimal Kalb-Ramond–Ricci coupling or a demonstration that it satisfies the vacuum field equations of the modified theory away from the shell.
  2. [§3] §3 (junction conditions): The Israel formalism is applied to the cut-and-paste construction, but the text does not address whether the Kalb-Ramond tensor itself contributes additional delta-function terms at the throat that would modify the surface stress-energy tensor.
  3. [§4–5] §4–5 (energy conditions and stability): All reported results for NEC/WEC/SEC violation, throat velocity, and linear stability rest on the unverified metric; without confirmation that the metric solves the modified Einstein equations, these calculations lack a controlled starting point.
minor comments (2)
  1. Notation for the Lorentz-violating parameter(s) should be defined once and used consistently; the abstract uses “parameters” while later sections appear to employ a single ℓ.
  2. The abstract’s phrasing “may give rise” should be replaced by a precise statement of what is assumed versus derived.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and indicate the revisions planned for the next version.

read point-by-point responses

  1. Referee: [§2] §2 (or equivalent): The modified black-hole metric f(r; ℓ) is introduced without an explicit derivation from the non-minimal Kalb-Ramond–Ricci coupling or a demonstration that it satisfies the vacuum field equations of the modified theory away from the shell.

    Authors: We acknowledge that an explicit derivation of the metric from the non-minimal coupling was omitted in the submitted version. In the revised manuscript we will insert a dedicated subsection deriving the modified black-hole solution from the action containing the non-minimal Kalb-Ramond–Ricci term. We will then verify by direct substitution that the resulting metric satisfies the vacuum field equations of the modified theory everywhere outside the thin shell. This addition will place the subsequent cut-and-paste construction on a firm footing. revision: yes

  2. Referee: [§3] §3 (junction conditions): The Israel formalism is applied to the cut-and-paste construction, but the text does not address whether the Kalb-Ramond tensor itself contributes additional delta-function terms at the throat that would modify the surface stress-energy tensor.

    Authors: We agree that the possible distributional contributions of the Kalb-Ramond background must be examined. In the revised §3 we will add a paragraph explaining that, for a constant vacuum expectation value and a metric that is continuous across the throat, the non-minimal coupling does not generate additional delta-function sources beyond those already captured by the standard Israel junction conditions. We will also state the precise form of the surface stress-energy tensor that results from this analysis. revision: yes

  3. Referee: [§4–5] §4–5 (energy conditions and stability): All reported results for NEC/WEC/SEC violation, throat velocity, and linear stability rest on the unverified metric; without confirmation that the metric solves the modified Einstein equations, these calculations lack a controlled starting point.

    Authors: We concur that the physical conclusions are meaningful only once the background metric is confirmed to solve the modified field equations. After incorporating the derivation and verification requested in the first comment, we will add an explicit statement at the opening of §4 that all subsequent results (energy conditions, geodesic motion, total exotic matter, throat evolution, and linear stability) rest on this verified solution. The numerical and analytic expressions will remain unchanged, but their domain of validity will be clearly delineated. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results follow from standard cut-and-paste on an externally assumed background metric.

full rationale

The paper takes the modified black-hole metric functions f(r; ℓ) as an input arising from prior non-minimal Kalb-Ramond–Ricci coupling (abstract: “may give rise to a modified black hole solution”). All subsequent steps—Israel junction conditions, surface stress-energy tensor, energy-condition evaluations, throat dynamics, and linear stability—are direct algebraic consequences of that metric and the standard thin-shell formalism. No quantity is fitted to data and then re-labeled a prediction, no self-referential definition appears, and no load-bearing step reduces to a self-citation whose content is itself unverified within the present work. The derivation chain is therefore self-contained once the background metric is granted.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central construction rests on the prior existence of the modified black hole metric and on the validity of the thin-shell approximation; no new particles or forces are postulated beyond the Kalb-Ramond background already present in string theory.

free parameters (1)
  • Lorentz-violating parameter(s)
    Strength of the Kalb-Ramond vacuum expectation value and its non-minimal coupling to the Ricci tensor; these control the modified metric and all subsequent wormhole properties.
axioms (2)
  • domain assumption A static spherically symmetric modified black hole solution exists for the non-minimal Kalb-Ramond-Ricci coupling.
    Invoked to supply the two background spacetimes that are joined at the throat.
  • domain assumption The thin-shell junction conditions of general relativity remain valid in the presence of the Kalb-Ramond background.
    Used to compute surface stress-energy and stability.

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