Non violation of energy conditions in wormholes modelling

Gauranga C. Samanta; Nisha Godani

arxiv: 1907.06726 · v1 · pith:QITGJQQAnew · submitted 2019-07-12 · 🌀 gr-qc

Non violation of energy conditions in wormholes modelling

Nisha Godani , Gauranga C. Samanta This is my paper

Pith reviewed 2026-05-24 22:47 UTC · model grok-4.3

classification 🌀 gr-qc

keywords traversable wormholesf(R) gravityenergy conditionsshape functionmodified gravityequation of state parameteranisotropic parameter

0 comments

The pith

A specific wormhole shape function satisfies energy conditions without violation when embedded in f(R) gravity for suitable parameter choices.

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

The paper examines traversable wormholes defined by the shape function b(r) = r0 tanh(r)/tanh(r0) inside an f(R) gravity model given by f(R) = R + α R^m - β R^{-n}. It computes the energy conditions, equation of state parameter, and anisotropic parameter for multiple choices of the four constants α, β, m, and n. A sympathetic reader cares because ordinary general relativity demands exotic matter that violates energy conditions to support traversable wormholes, whereas this modified-gravity setting can avoid such violations by adjusting the function parameters.

Core claim

For the shape function b(r) = r0 tanh(r)/tanh(r0) in f(R) gravity with f(R) = R + α R^m - β R^{-n}, different real values of the constants α, β, m, and n yield cases in which the null, weak, strong, and dominant energy conditions hold, while the equation of state parameter and anisotropic parameter take determined values.

What carries the argument

The shape function b(r) = r0 tanh(r)/tanh(r0) together with the four-parameter f(R) model, which together determine the stress-energy tensor components and thereby control whether energy conditions are satisfied.

If this is right

Energy conditions hold without violation for multiple distinct choices of the constants in f(R).
The equation of state parameter takes definite values determined by the same constants.
The anisotropic parameter is fixed once the constants are chosen.
The geometry remains traversable while the stress-energy tensor satisfies the standard energy inequalities.

Where Pith is reading between the lines

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

If the same shape function is inserted into other modified-gravity theories, similar parameter tuning might also remove energy-condition violations.
The result suggests that the requirement for exotic matter in wormhole physics is not universal but depends on the gravitational action chosen.
One could test whether the same shape function produces stable wormhole solutions by examining the second variation of the action or by adding small perturbations.

Load-bearing premise

The chosen shape function generates a traversable wormhole geometry whose energy conditions can be made non-violating simply by picking appropriate real numbers for the four constants in f(R).

What would settle it

Explicit numerical evaluation of the energy-condition expressions for a concrete set of α, β, m, n values that the paper claims works, followed by direct checking that all four conditions remain non-negative throughout the wormhole throat region.

Figures

Figures reproduced from arXiv: 1907.06726 by Gauranga C. Samanta, Nisha Godani.

**Figure 2.** Figure 2: Case 2: Plots for Density, NEC, DEC, 4 & ω with f(R) = R + αRm 16 [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗

**Figure 3.** Figure 3: Case 3: Plots for Density, NEC, DEC, 4 & ω with f(R) = R − βR−n 17 [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗

**Figure 4.** Figure 4: Case 4: Plots for Density, NEC, DEC, 4 & ω with f(R) = R + αRm − βR−n 18 [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗

read the original abstract

Morris \& Thorne \cite{morris1} proposed geometrical objects called traversable wormholes that act as bridges in connecting two spacetimes or two different points of the same spacetime. The geometrical properties of these wormholes depend upon the choice of the shape function. In literature, these are studied in modified gravities for different types of shape functions. In this paper, the traversable wormholes having shape function $b(r)=\frac{r_0\tanh(r)}{\tanh(r_0)}$ are explored in $f(R)$ gravity with $f(R)=R+\alpha R^m-\beta R^{-n}$, where $\alpha$, $\beta$, $m$ and $n$ are real constants. For different values of constants in function $f(R)$, the analysis is done in various cases. In each case, the energy conditions, equation of state parameter and anisotropic parameter are determined.

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.

Desk Editor's Note private letter to a colleague

This paper adds one more explicit example of a wormhole in f(R) gravity where energy conditions hold after tuning parameters, but introduces no new framework.

read the letter

The paper is basically an existence proof by example: they pick a shape function that flares out properly at the throat and is asymptotically flat, put it in a standard f(R) gravity model with four free constants, and show that for some values of those constants the null, weak, strong, and dominant energy conditions are satisfied along with the other quantities they track. What is new is the specific form of the shape function, b(r) = r0 tanh(r)/tanh(r0). The f(R) form is already used in wormhole papers, and the method of checking energy conditions case by case is common. They do a decent job laying out the different cases for the constants and computing the results for each. The main limitation is that the constants are free and are varied until the conditions hold. This is not unusual in the field, but it means the result is that non-violation is possible rather than that it must happen or happens for natural values. The paper does not provide any external constraint or prediction that would make the choice of constants less arbitrary. A reader who follows wormhole constructions in modified gravity will find this a useful addition to the list of working examples. Someone looking for new ideas or connections to observations will not. The work is coherent and the claim is limited to what the calculations show, so it should go to peer review. The referee can verify the numerical or algebraic results for the cases presented.

Referee Report

0 major / 3 minor

Summary. The manuscript investigates traversable wormholes with the specific shape function b(r) = r_0 tanh(r)/tanh(r_0) in f(R) gravity, taking f(R) = R + α R^m - β R^{-n}. It performs case-by-case analysis by assigning different values to the free parameters α, β, m, n, and reports the resulting energy conditions (NEC, WEC, SEC, DEC), equation-of-state parameter, and anisotropy parameter for each case. The geometric requirements (throat, flaring-out, asymptotic flatness) are stated to be satisfied by the shape function independently of the f(R) parameters.

Significance. If the explicit calculations hold, the work supplies concrete, parameter-tuned examples of wormhole solutions in f(R) gravity for which all standard energy conditions can be satisfied. This is a modest but useful addition to the literature on modified-gravity wormholes, especially because the chosen shape function decouples the geometric constraints from the matter-sector tuning. The paper does not claim a general proof or parameter-free result, so its scope remains appropriately limited.

minor comments (3)

[Abstract] Abstract: the phrase 'the energy conditions ... are determined' is vague; a single explicit numerical example (e.g., one set of α, β, m, n together with the resulting ρ, p_r, p_t and the four energy-condition inequalities) would make the central claim immediately verifiable.
[Field equations / Results] The manuscript should state the precise expressions for the energy density and pressures that follow from the f(R) field equations before presenting the numerical cases; without these, the reader cannot reproduce or check the reported signs of the energy conditions.
[Model section] Notation: the four constants are introduced as 'real constants' without any domain restrictions or stability considerations; adding a brief remark on the ranges explored would improve transparency.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No major comments were listed in the report, so we have no specific points requiring point-by-point rebuttal or revision at this stage.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper selects the shape function b(r)=r0 tanh(r)/tanh(r0) and the f(R) form R + α R^m - β R^{-n} by explicit choice, then computes energy conditions, EoS parameter, and anisotropy for selected numerical values of the four constants across cases. This is a direct parametric evaluation of the chosen model; the output quantities are computed from the inputs rather than presented as independent predictions that reduce to the fit by construction. No self-citation chain, uniqueness theorem, or ansatz smuggling is invoked as load-bearing. The geometric wormhole conditions (throat, flaring-out, asymptotic flatness) hold by the shape function alone and are independent of the f(R) parameters. The manuscript therefore reports an existence result via parameter tuning, which is self-contained and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

The model rests on four free parameters in f(R) that are adjusted per case and on the standard Morris-Thorne ansatz; no independent evidence for the chosen shape function is given.

free parameters (4)

α
Coefficient of the R^m term; varied across cases to satisfy energy conditions
β
Coefficient of the R^{-n} term; varied across cases
m
Exponent of the positive-power term; chosen per case
n
Exponent of the negative-power term; chosen per case

axioms (2)

domain assumption Morris-Thorne metric ansatz for static spherically symmetric traversable wormholes
Invoked as the geometric framework without derivation
standard math f(R) gravity field equations derived from the action integral
Standard modified-gravity starting point

pith-pipeline@v0.9.0 · 5678 in / 1262 out tokens · 25273 ms · 2026-05-24T22:47:56.881044+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel contradicts

?

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

For different values of constants in function f(R), the energy conditions... are determined... f(R)=R+αR^m−βR^{-n}, where α,β,m and n are real constants.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the traversable wormholes having shape function b(r)=r0 tanh(r)/tanh(r0) are explored in f(R) gravity

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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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