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arxiv: 2606.00178 · v2 · pith:OED3LRORnew · submitted 2026-05-29 · 🌀 gr-qc

Traversable Wormholes Supported by Entropy-Inspired Effective Matter Sectors

Jonathan A. Rebou\c{c}as , Francisco Bento Lustosa , Celio R. Muniz This is my paper

Pith reviewed 2026-06-28 21:25 UTC · model grok-4.3

classification 🌀 gr-qc
keywords traversable wormholesMorris-Thorne metricmodified entropyBarrow entropyTsallis entropyenergy conditionsbarotropic equation of state
0
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The pith

Modified entropy profiles from Barrow, Tsallis, Kaniadakis, logarithmic, and exponential deformations can serve as effective sources for traversable wormholes.

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

The paper tests whether density profiles generated by the entropy-geometry correspondence from modified Bekenstein-Hawking entropies can function as phenomenological matter sources inside the Morris-Thorne wormhole metric. It isolates the radial density from each entropy model, adopts a barotropic equation of state for the radial pressure, and solves the remaining field equations for the shape function, redshift function, and tangential pressure. Regular solutions appear in all five sectors, with the required null-energy-condition violation at the throat always coinciding with the geometric flare-out condition while the tangential and strong-energy conditions reveal how the anisotropy redistributes the exoticity. The Tolman-Oppenheimer-Volkoff equilibrium balance changes its sign pattern in a sector-dependent way. A sympathetic reader would care because the construction shows that thermodynamic deformations of gravity can directly supply the matter content needed for wormhole throats without separate ad-hoc assumptions about exotic fluids.

Core claim

The entropy-geometry correspondence maps each modified Bekenstein-Hawking entropy to an effective radial density profile; when these profiles are inserted into the Morris-Thorne line element together with the barotropic relation p_r = w ho, the resulting configurations satisfy the Einstein equations at the throat for the Barrow, Tsallis, Kaniadakis, logarithmic, and exponential cases, with energy-condition behavior and hydrostatic balance determined by the specific entropy deformation.

What carries the argument

The entropy-geometry correspondence that converts a chosen modified Bekenstein-Hawking entropy into an effective anisotropic matter sector, here supplying only the radial density profile for Morris-Thorne reconstruction.

If this is right

  • Barrow and Tsallis entropies produce algebraic negative-density sources.
  • Kaniadakis and exponential entropies produce localized density profiles.
  • The logarithmic sector admits both negative-density and positive-density phantom-like regimes.
  • In every regular solution the radial null-energy-condition violation at the throat is required by the flare-out condition.
  • The Tolman-Oppenheimer-Volkoff balance exhibits sector-dependent reversals of the signs of the gravitational and compensating-pressure terms.

Where Pith is reading between the lines

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

  • If the correspondence is robust, similar entropy deformations could be tested as sources for other exotic spacetimes whose field equations also demand negative energy densities.
  • Stability analysis under linear perturbations would reveal which entropy sectors produce wormholes that persist long enough to be astrophysically relevant.
  • Observational constraints on the redshift function or the flare-out parameter could be translated back into bounds on the deformation parameters of the underlying entropies.

Load-bearing premise

The radial density profiles obtained from the modified entropies via the entropy-geometry correspondence can be used directly as phenomenological sources in the Morris-Thorne geometry once a barotropic equation of state is supplied.

What would settle it

An explicit calculation showing that none of the five derived density profiles simultaneously satisfies the Einstein equations and the flare-out condition at the throat would falsify the claim that these entropy sectors provide viable sources.

Figures

Figures reproduced from arXiv: 2606.00178 by Celio R. Muniz, Francisco Bento Lustosa, Jonathan A. Rebou\c{c}as.

Figure 1
Figure 1. Figure 1: FIG. 1. The Barrow-inspired density profile, [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The geometric behavior of the Barrow-inspired wormhole for different values of the deformation parameter [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Embedding structure of the Barrow-inspired wormhole geometry for different values of the deformation parameter [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Behavior of the energy conditions for the Barrow-inspired wormhole, with [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Equilibrium forces for the Barrow-inspired wormhole as functions of the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The Tsallis-inspired density profile, [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The geometric behavior of the Tsallis-inspired wormhole for different values of the deformation parameter [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Embedding structure of the Tsallis-inspired wormhole geometry for different values of the deformation parameter [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Behavior of the energy conditions for the Tsallis-inspired wormhole, with [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Equilibrium forces for the Tsallis-inspired wormhole as functions of the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. The Kaniadakis-inspired density profile, [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. The geometric behavior of the Kaniadakis-inspired wormhole for different values of the parameter [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Embedding structure of the Kaniadakis-inspired wormhole geometry for different values of the parameter [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Behavior of the energy conditions for the Kaniadakis-inspired wormhole, with [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Equilibrium forces for the Kaniadakis-inspired wormhole as functions of the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p024_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. The Logarithmic-inspired density profile, [PITH_FULL_IMAGE:figures/full_fig_p025_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. The geometric behavior of the Logarithmic-inspired wormhole for different values of the parameter [PITH_FULL_IMAGE:figures/full_fig_p025_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Embedding structure of the Logarithmic-inspired wormhole geometry for different values of the parameter [PITH_FULL_IMAGE:figures/full_fig_p027_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Behavior of the energy conditions for the logarithmic-inspired wormhole, with [PITH_FULL_IMAGE:figures/full_fig_p028_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. Equilibrium forces for the logarithmic-inspired wormhole as functions of the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p029_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21. The exponential-inspired density profile, [PITH_FULL_IMAGE:figures/full_fig_p030_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22. The geometric behavior of the exponential-inspired wormhole for different values of the parameter [PITH_FULL_IMAGE:figures/full_fig_p031_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23. Embedding structure of the exponential-inspired wormhole geometry for different values of the parameter [PITH_FULL_IMAGE:figures/full_fig_p032_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: FIG. 24. Behavior of the energy conditions for the exponential-inspired wormhole, with [PITH_FULL_IMAGE:figures/full_fig_p033_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: FIG. 25. Equilibrium forces for the exponential-inspired wormhole as functions of the radial coordinate [PITH_FULL_IMAGE:figures/full_fig_p034_25.png] view at source ↗
read the original abstract

The entropic interpretation of gravity suggests that spacetime geometry may encode thermodynamic information associated with microscopic degrees of freedom. In this context, the entropy--geometry correspondence of Refs.[1,2] links modified Bekenstein--Hawking entropies to deformed black-hole geometries and effective anisotropic matter sectors. Motivated by this result, we test whether these entropy-induced density profiles can act as phenomenological sources for traversable wormholes. Here we use the density sector as the thermodynamic input for a Morris--Thorne reconstruction, thereby isolating the role of the entropy-induced radial profile. The radial pressure follows from a barotropic equation of state, $p_r=w\rho$, while the remaining variables are determined by the wormhole field equations and anisotropic equilibrium. We analyze five entropy-inspired sectors: Barrow, Tsallis, Kaniadakis, logarithmic, and exponential. Barrow and Tsallis are algebraic negative-density sources; Kaniadakis and exponential profiles are localized; and the logarithmic sector admits negative-density and positive-density phantom-like regimes. In all regular configurations, radial null-energy-condition violation at the throat is tied to the flare-out condition, while the tangential null energy condition and the strong-energy-condition combination diagnose the anisotropic redistribution of exoticity. The TOV balance is sector dependent: in the Barrow and Kaniadakis branches, the gravitational and compensating pressure contributions can reverse their signs together while remaining balanced; the other branches retain a common sign pattern with different degrees of near-throat localization. This framework shows that modified entropy profiles can provide viable effective sources for traversable wormholes, with the supporting mechanism depending sensitively on the underlying entropy deformation.

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

0 major / 3 minor

Summary. The paper claims that density profiles obtained from modified Bekenstein-Hawking entropies (Barrow, Tsallis, Kaniadakis, logarithmic, and exponential sectors) via the entropy-geometry correspondence can serve as viable phenomenological sources for Morris-Thorne traversable wormholes. With radial density fixed by each entropy sector, a barotropic EOS p_r = w ρ imposed, the shape function b(r) integrated from the Einstein (tt) equation, the redshift Φ(r) solved from the (rr) equation, and p_t determined from anisotropic equilibrium, the authors report regular solutions satisfying b(r0) = r0, b'(r0) < 1 (linked to radial NEC violation at the throat), and TOV balance in all five sectors, with sector-dependent patterns in energy-condition violation and gravitational/pressure contributions.

Significance. If the constructions hold, the work supplies a concrete phenomenological bridge between entropic gravity modifications and wormhole spacetimes, showing that entropy-deformed radial densities can support traversable configurations without further ad-hoc fields. The explicit sector-by-sector verification of flare-out, NEC violation tied to b'(r0)<1, and TOV equilibrium constitutes a strength, as does the demonstration that supporting mechanisms (sign patterns of gravitational vs. pressure terms) vary sensitively with the entropy deformation. This adds falsifiable, sector-specific predictions to the literature on exotic-matter sources.

minor comments (3)
  1. [Abstract] Abstract: the statement that 'all sectors yield regular configurations' would be strengthened by a brief indication of the range of w values that produce regularity, since the barotropic parameter is the sole free parameter listed in the axiom ledger.
  2. The manuscript should include a compact table (perhaps in §4 or §5) summarizing, for each entropy sector, the adopted w, the resulting b'(r0), and the sign pattern of the TOV terms near the throat; this would make the sector-dependent claims immediately verifiable.
  3. Notation: the entropy-geometry correspondence is invoked from Refs.[1,2] without restating the explicit map from entropy to ρ(r); a short appendix or paragraph recalling the functional form of ρ(r) for each sector would improve self-contained readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our manuscript, as well as for the favorable assessment of its significance. The report correctly identifies the central construction (entropy-deformed radial densities as sources for Morris-Thorne wormholes) and the sector-dependent features we report. No major comments were raised.

Circularity Check

0 steps flagged

No significant circularity; phenomenological test with independent inputs

full rationale

The derivation takes modified-entropy density profiles as external inputs from the entropy-geometry correspondence, adopts the standard barotropic ansatz p_r = w ρ with sector-specific constant w, integrates the Morris-Thorne shape function b(r) from the Einstein (tt) equation, solves for the redshift function from the (rr) equation, and obtains p_t from the anisotropic TOV equation. It then verifies that regular solutions satisfying b(r0)=r0, b'(r0)<1, and the flare-out condition exist for appropriate w choices, with energy-condition behavior following directly from the Einstein equations and the chosen ρ(r). No step reduces the target wormhole viability to a fit or self-definition of the output quantities; the construction is a standard phenomenological reconstruction rather than a closed loop. Self-citations to the prior correspondence supply the input densities but do not bear the load of the wormhole-supporting mechanism or the reported energy-condition diagnostics.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The claim rests on the entropy-geometry correspondence supplying usable density profiles, the Morris-Thorne metric ansatz, and a barotropic closure for radial pressure; these are standard in the domain but introduce free parameters whose values are sector-dependent.

free parameters (1)
  • w
    Barotropic index in p_r = w ρ, selected per entropy sector to close the system and satisfy equilibrium.
axioms (2)
  • domain assumption Morris-Thorne metric ansatz for static spherically symmetric wormholes
    Provides the geometric framework into which the entropy-derived densities are inserted.
  • domain assumption Entropy-geometry correspondence of Refs.[1,2] yields valid effective density profiles
    Supplies the thermodynamic input used for the wormhole reconstruction.

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Reference graph

Works this paper leans on

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    Energy conditions and equilibrium in the Barrow-inspired sector The radial pressure is fixed by the chosen equation of state, pr,B(r) =w BρB(r).(59) However, as discussed in the general construction, the parameterwB cannot be chosen independently if the redshift function is required to be regular at the throat. For the Barrow-inspired shape function, one ...

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    Geometry induced by the Tsallis-inspired profile The Tsallis entropy modifies the standard additive structure of horizon thermodynamics through the non-extensive parameterδ[62]. In the entropy–geometry correspondence of Ref. [1], the associated effective density is ρT (r) =− M π−δ(δ−1) 2δ r−2δ−1,(68) 14 FIG. 5. Equilibrium forces for the Barrow-inspired w...

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    Energy conditions and equilibrium in the Tsallis-inspired sector The radial pressure is fixed by the chosen equation of state, pr,T(r) =w T ρT (r).(72) As in the Barrow-inspired sector, the equation-of-state parameter cannot be chosen independently if the redshift function is required to be regular at the throat. For the Tsallis-inspired shape function, o...

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    Energy conditions and equilibrium in the Kaniadakis-inspired sector The radial pressure is fixed by the chosen equation of state, pr,κ(r) =w κρκ(r).(85) As in the previous sectors, the equation-of-state parameter is not arbitrary once the regularity of the redshift derivative at the throat is imposed. For the Kaniadakis-inspired shape function, one has b′...

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