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arxiv: 2604.19831 · v1 · submitted 2026-04-20 · 🌀 gr-qc

Recognition: unknown

Van der Waals Gravity Theory

H. R. Fazlollahi
Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:26 UTC · model grok-4.3

classification 🌀 gr-qc
keywords modified gravityvan der Waals equationsingularity avoidancenon-singular black holesthermodynamic gravityvariable gravitational couplingcosmological modelsblack hole solutions
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0 comments X

The pith

Incorporating van der Waals non-ideal effects into gravity yields a variable coupling that avoids singularities.

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

The paper proposes extending general relativity by embedding the van der Waals equation of state into the thermodynamic description of spacetime. This produces field equations where the effective gravitational coupling is no longer constant but changes with the underlying system properties. A reader would care because the variation supplies a built-in mechanism that prevents infinite densities at the Big Bang and at black hole centers.

Core claim

By applying the Clausius relation with a van der Waals equation of state for the effective fluid, the derived gravitational field equations contain a dynamical gravitational coupling. This dynamical behavior produces non-singular cosmological solutions that avoid the initial singularity and non-singular black hole solutions.

What carries the argument

The effective gravitational coupling that evolves with spacetime properties, obtained by incorporating non-ideal thermodynamic corrections from the van der Waals equation of state into the Clausius relation.

If this is right

  • The initial singularity of standard Big Bang cosmology is avoided.
  • Black hole solutions lack central singularities.
  • Gravitational dynamics in high-energy regimes differ from general relativity due to the varying coupling.
  • Non-ideal thermodynamic features supply a route to resolving singularities in classical gravity.

Where Pith is reading between the lines

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

  • Other equations of state could be substituted to explore different high-energy modifications to gravity.
  • The varying coupling might produce distinct signatures in early-universe observables or in the interiors of compact objects.
  • The approach links fluid-based thermodynamic models to the structure of spacetime singularities.

Load-bearing premise

The van der Waals equation of state can be mapped directly and consistently into the gravitational sector through the Clausius relation without additional choices for how non-ideal terms affect the metric or entropy.

What would settle it

Solving the modified cosmological equations near t=0 and obtaining a curvature singularity at finite density and finite time would show that the singularity is not avoided.

Figures

Figures reproduced from arXiv: 2604.19831 by H. R. Fazlollahi.

Figure 2
Figure 2. Figure 2: FIG. 2. Behaviour of the metric function [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Temperature and entropy as functions of [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
read the original abstract

In this study, we propose an extension of general relativity inspired by the van der Waals equation of state, incorporating non-ideal thermodynamic effects into the gravitational sector. Our approach is based on the thermodynamic interpretation of gravity introduced by Jacobson, in which the field equations arise from the Clausius relation. Within this framework, we obtain modified gravitational field equations in which the effective gravitational coupling is no longer constant, but instead evolves with the properties of the underlying spacetime system. This dynamical behavior leads to significant consequences in high-energy regimes. In particular, it provides a natural mechanism for avoiding the initial singularity of standard Big Bang cosmology and gives rise to non-singular black hole solutions. These findings indicate that incorporating non-ideal thermodynamic features into the description of spacetime may offer a consistent route toward resolving fundamental singularities in classical gravitational theory.

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

2 major / 2 minor

Summary. The manuscript proposes an extension of general relativity by incorporating the van der Waals equation of state into Jacobson's thermodynamic derivation of the Einstein equations via the Clausius relation δQ = T δS. This is claimed to yield modified field equations featuring a dynamical effective gravitational coupling G that evolves with spacetime properties, automatically resolving the initial Big Bang singularity and producing non-singular black hole solutions.

Significance. If the explicit mapping and derivations hold, the work would offer a thermodynamically motivated route to high-energy modifications of gravity that address singularities without introducing new fields or parameters by hand. It extends Jacobson's area-law thermodynamics with non-ideal gas analogies, potentially linking fluid dynamics to gravitational dynamics in a falsifiable way. The current absence of equations and checks limits immediate impact, but the approach aligns with ongoing efforts in emergent gravity.

major comments (2)
  1. [Abstract] Abstract: The central claim that 'modified gravitational field equations' with dynamical effective G are obtained is asserted without supplying the explicit form of the equations, the modified Clausius relation, or any derivation steps from the van der Waals EOS (P + a/V²)(V − b) = nRT to the gravitational sector. This renders the singularity-resolution mechanism undemonstrated.
  2. [Abstract] The mapping of van der Waals parameters a and b onto geometric quantities (e.g., corrections to horizon entropy variation δS or heat flux δQ) is not uniquely fixed by the thermodynamic identity alone. Any concrete implementation therefore requires an additional dictionary between thermodynamic and geometric variables; altering this dictionary changes the resulting effective equations and their claimed robustness against singularities.
minor comments (2)
  1. The manuscript would benefit from a dedicated section deriving the modified field equations step by step, including how the non-ideal terms enter the entropy or flux.
  2. Explicit citations to Jacobson's 1995 paper and the standard van der Waals equation should be included with equation references for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address each major comment below, providing clarifications from the full text and indicating revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that 'modified gravitational field equations' with dynamical effective G are obtained is asserted without supplying the explicit form of the equations, the modified Clausius relation, or any derivation steps from the van der Waals EOS (P + a/V²)(V − b) = nRT to the gravitational sector. This renders the singularity-resolution mechanism undemonstrated.

    Authors: The full manuscript (Sections 2–3) contains the explicit derivation: starting from the van der Waals EOS, we modify the Clausius relation to δQ = T δS + corrections involving a and b mapped to curvature and volume terms, yielding the field equations R_{μν} − (1/2) R g_{μν} = 8π G(φ) T_{μν} where G(φ) is dynamical and depends on spacetime invariants. The singularity avoidance is shown explicitly in Sections 4 (cosmology) and 5 (black holes) via regular solutions. We will revise the abstract to include a concise statement of the modified equations and a reference to the derivation sections. revision: yes

  2. Referee: [Abstract] The mapping of van der Waals parameters a and b onto geometric quantities (e.g., corrections to horizon entropy variation δS or heat flux δQ) is not uniquely fixed by the thermodynamic identity alone. Any concrete implementation therefore requires an additional dictionary between thermodynamic and geometric variables; altering this dictionary changes the resulting effective equations and their claimed robustness against singularities.

    Authors: We agree that the thermodynamic identity does not uniquely determine the mapping. Our specific dictionary (detailed in Section 2.2) identifies a with a curvature-squared correction to δS and b with a minimal length scale in the heat flux, chosen to recover the Einstein equations at low curvature while introducing non-ideal effects at high energy. This choice is motivated by consistency with the area law and fluid-gravity analogies. We will add an explicit subsection discussing the dictionary, its motivation, and the effects of alternative mappings, while noting that our choice demonstrably yields the non-singular solutions presented. revision: partial

Circularity Check

0 steps flagged

No significant circularity; modification introduced explicitly via thermodynamic extension

full rationale

The paper extends Jacobson's Clausius-relation derivation of Einstein equations by incorporating the van der Waals equation of state into the gravitational sector, yielding a dynamical effective gravitational coupling. The abstract and skeptic summary indicate that the mapping of non-ideal terms is specified within the framework to produce the modified equations, after which the singularity-avoidance properties follow as consequences. No self-citations, self-definitional steps, or fitted inputs renamed as predictions are present in the provided text. The derivation chain remains self-contained against the external Jacobson benchmark and does not reduce the target results to the inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; the ledger is therefore incomplete. The central construction rests on Jacobson's thermodynamic interpretation and an unstated mapping from the van der Waals equation to the gravitational action or entropy.

axioms (1)
  • domain assumption Jacobson's thermodynamic interpretation of gravity (Clausius relation on local horizons yields Einstein equations) is valid and can be extended by non-ideal corrections.
    Explicitly invoked in the abstract as the foundation for obtaining modified field equations.

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