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REVIEW 3 major objections 5 minor 3 cited by

Negative-mass objects may appear naturally around compact stars, repelling light and ordinary matter while still forming bound systems with positive-mass stars.

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2026-08-02 23:45 UTC pith:HSPQUVAN

load-bearing objection The formal modified-gravity constructions are competent reverse engineering, but the standard-gravity route to negative mass objects fails on a sign error: Eq. (42) does not follow from Eqs. (39)+(41), and the corrected coefficient gives positive m in the stated parameter range. the 3 major comments →

arxiv 2602.15058 v2 pith:HSPQUVAN submitted 2026-02-13 gr-qc astro-ph.COhep-th

May Negative Mass Objects exist in the sky?

Shin'ichi Nojiri , S.D. Odintsov This is my paper
classification gr-qc astro-ph.COhep-th MSC 83C5783C1083D0585A15 PACS 04.20.-q04.50.Kd95.30.Sf98.80.-k
keywords negative mass objectanti-gravitycosmological fluidnegative cosmological constantTolman-Oppenheimer-Volkoff equationsscalar-Einstein-Gauss-Bonnet gravitygravitational lensingtwo-scalar model
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that negative-mass objects (NMOs) are not as exotic as usually assumed. The authors claim that when a compact positive-mass object sits in a cosmological fluid with negative pressure and a negative cosmological constant, the fluid it pushes away can outweigh the object itself, leaving a net negative gravitational mass. They support this with a deficit-mass estimate, with asymptotic solutions of the full Tolman-Oppenheimer-Volkoff equations, and with explicit modified-gravity models (a two-scalar theory and scalar-Einstein-Gauss-Bonnet gravity) that realize NMO geometries. They then show that such an NMO acts as a gravitational concave lens and can form a stable bound two-body system with an ordinary star, because a negative inertial mass makes the otherwise repulsive force centripetal. If correct, this would give a concrete route to effective anti-gravity and to systems whose gravitational mass is screened by a cloud of NMOs.

Core claim

On the paper's own terms, the central discovery is a mechanism: a positive-mass body immersed in a fluid with equation-of-state parameter w in a spacetime with negative cosmological constant displaces the fluid, and the displaced mass M_lost can exceed the body's mass M. The total mass, M_total = M - M_lost (with M_lost = 32πM³ρ0 for a specific modified equation of state), becomes negative when 32πM²ρ0 > 1. The paper further claims that solving the TOV equations asymptotically gives an enclosed mass m ∝ (Λ/κ²) r³ whose sign can be negative for certain w, that modified-gravity models can realize the corresponding NMO metric exactly, and that in Newtonian mechanics a positive and negative mass

What carries the argument

The load-bearing mechanism is the mass-deficit accounting: on a fixed Schwarzschild background with metric e^{2ν}=1-2M/r, a perfect fluid with negative pressure satisfies ρ=ρ0 e^{-(1+w)/w ν}, so its density rises with radius and the fluid is pushed out by the compact object. The lost mass M_lost is the integral of the density deficit from r=2M to a cutoff, and for a tuned equation of state it evaluates to 32πM³ρ0, making the total mass M-32πM³ρ0 negative when 32πM²ρ0>1. In the modified-gravity constructions, the key object is a reconstruction formula that algebraically determines the scalar potentials (two-scalar model or Gauss-Bonnet coupling) from a prescribed metric, so the NMO metric e^{

Load-bearing premise

The claim that a compact star can turn itself into a negative-mass object hinges on treating the mass of displaced fluid as a simple deficit subtracted from the star's mass on a fixed Schwarzschild background; if back-reaction of the fluid on the geometry changes this accounting, the negative total mass need not follow — and the paper's own corrected asymptotic TOV equations actually give a positive enclosed mass for -1 < w < -2/3.

What would settle it

Numerically integrate the full TOV system (Eqs. 27 and 30) for a compact object of mass M in a fluid with w=-2/3 and Λ<0, with suitable boundary conditions, and check whether the enclosed mass m(r) becomes negative anywhere outside the object; if it does not, the deficit-mass estimate leading to M_total < 0 is not realized in the full theory.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If NMOs exist, they would act as gravitational concave lenses, producing dark spots or distorted images of background sources instead of Einstein rings.
  • A star and a surrounding NMO can form a bound two-body system; observationally this would appear as periodic flashing of background light as the pair orbits its common centre of mass.
  • Clouds of NMOs around a galaxy would screen its gravitational mass, making the system nearly gravitationally invisible while still lensing light.
  • The paper's density threshold for solar-mass NMOs, ρ0 ≳ 10^18 kg/m³, implies the effect is negligible for typical cosmological densities unless the fluid is strongly clustered.
  • If a supernova or black-hole merger happens near NMOs, the emitted energy flux would be modified by the repulsive force from the NMO.

Where Pith is reading between the lines

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

  • The paper's asymptotic TOV result appears to contain an algebraic slip: combining its own Eqs. (39) and (41) gives an enclosed mass that is positive in the window -1<w<-2/3, so the negative-mass conclusion in that section rests on the deficit-bookkeeping rather than on the full back-reacted solution.
  • If the deficit mechanism fails, the modified-gravity constructions remain: they formally realize NMO metrics as exact solutions, so the physical existence question shifts to whether the required scalar couplings can arise from a UV-complete theory.
  • A testable extension is to search for gravitationally invisible galaxies where the lensing mass is much larger than the dynamical mass; the paper's screening picture predicts a specific concave-lensing signature alongside reduced gravitational binding.
  • The vanishing-mass black hole with a finite shadow radius suggests a new observational class: objects that cast a shadow yet exert no net gravitational pull, distinguishable from standard black holes by the unusual ratio of shadow radius to horizon radius.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper conjectures that negative mass objects (NMOs) can exist in the sky. The central claim is that NMOs appear as solutions of standard Einstein gravity when a compact positive-mass object is embedded in a cosmological fluid with negative pressure and a negative cosmological constant (§II). The paper also constructs modified-gravity models (a two-scalar theory and a scalar-Einstein-Gauss-Bonnet theory) in which a Hayward-type NMO metric is realized by reconstruction, and it studies photon orbits, massive-particle orbits, Newtonian bound states of positive and negative masses, observational signatures, and a vanishing-mass object (§IV–VIII).

Significance. If the central claim were correct, the paper would be significant for gravitational lensing, dark-matter phenomenology, and the theoretical viability of exotic compact objects. The paper provides explicit analytic metrics and a detailed Newtonian two-body analysis of positive/negative mass systems. However, the standard-gravity derivation in §II.B contains an algebraic error that reverses the sign of the asymptotic mass, and the modified-gravity constructions in §III are formal reconstructions rather than independent evidence. No reproducible code or machine-checked proofs are provided. The main value of the paper is as a catalogue of explicitly constructed toy models and classical-mechanics illustrations, not as a demonstration that NMOs arise from standard gravitational equations.

major comments (3)
  1. [§II.B, Eqs. (39)–(42)] Combining Eq. (39) with Eq. (41) does not yield Eq. (42). Substituting ρ0 = Λ/(κ²(1+3w)) into (39) gives m ∼ 2π(1+w)/(1+3w) Λ/κ² r³, not m ∼ (4π/3)(2+3w)/(1+3w) Λ/(2κ²) r³. For the announced fluid range 0 > w > -1, ρ0 > 0 and Λ < 0 require -1 < w < -1/3, where 1+w > 0 and 1+3w < 0, so the coefficient is negative and the asymptotic mass is positive for every such w. The negative-mass solution claimed in Eq. (42) and the text following it therefore does not follow. This is the load-bearing step of the paper's standard-gravity argument.
  2. [§II.A, Eqs. (8), (15)–(17); §VII] The earlier 'lost mass' calculation is performed on a fixed Schwarzschild background and subtracts a fluid deficit from the point mass without including back-reaction. The full back-reaction treatment in §II.B, which is the paper's direct standard-gravity route, fails as shown above. Moreover, §VII shows that the condition for negative total mass requires ρ0 ≳ 10^18 kg·m^-3, a fine-tuning the paper itself acknowledges. Thus the only standard-gravity mechanism for NMOs is unsupported.
  3. [§III.A, §III.C; §IX] The modified-gravity models are constructed by solving for the action functions (A, B, C, V in the two-scalar model; A, V, f in scalar-Einstein-Gauss-Bonnet gravity) in terms of the desired metric, so the NMO metric is a solution by construction. The stability and ghost-freeness are imposed via Lagrange-multiplier constraints (50) and (73) that freeze the scalar fields; this does not show that NMOs are natural or generic. The paper itself states in §IX that these are 'just a formal solution.' This cannot independently support the existence claim.
minor comments (5)
  1. [Throughout] Typos: 'NWOs' in §IX should be 'NMOs'; 'distingusihed' in §VII; 'Subsection SectionIIIA' and 'SectionIIIB' in §VIII are malformed cross-references.
  2. [§IV, Eq. (82)] The assertion U'(r) < 0 is not derived; since the first term of U is manifestly decreasing but the second term's derivative is sign-indefinite, a short derivation would improve readability.
  3. [§VI] The statement that 'the point mass with m1 suffers a repulsive force from the point mass with m2' is confusing but internally consistent when one accounts for the negative inertial mass. The relative-motion equation r_ddot = -G(m1+m2) r/r³ is independent of the negative sign, so the bound-state analysis is sound conditional on the existence of an NMO.
  4. [§II.B] The symbol ρ0 is used both for the asymptotic fluid density in Eq. (6) and for the constant coefficient in the asymptotic expansion in the TOV system; the paper should disambiguate these usages.
  5. [§VII–IX] The conjectured observational signatures are qualitative (flashing light, screening, holes in rocks) and are not developed to the level of a falsifiable prediction. This is appropriate for a speculative paper, but it should be labeled as such more prominently.

Circularity Check

2 steps flagged

Modified-gravity NMO is a reconstruction, not a prediction, and its stability is imported from the authors' own prior papers; the central standard-gravity argument is independent but algebraically flawed.

specific steps
  1. self definitional [Section III.A.2, Eqs. (51)-(55)]
    "The equations (51) are algebraically solved with respect to A, B, C, and V below... This shows that one can construct a model which realises the spacetime defined by the metric (47) by finding (t, r)-dependence of ρ and p and by replacing (t, r) in Eq. (53) with (ϕ, χ). ... As an NMO, we consider the following e^{2ν}=e^{-2λ}=1+2Mr^2/(r^3+2Mλ^2)."

    The action functions A,B,C,V are solved from the Einstein equations for the chosen NMO metric (55). The statement that the model 'realises' the NMO is therefore true by construction: the target metric is the input, and the solution is the output. This cannot independently show that NMOs are generic or natural in the two-scalar or scalar-GB theory. The paper's own §IX concedes this is 'just a formal solution', which makes the step an admitted reconstruction rather than a hidden fit, but the supporting evidence is still tautological.

  2. self citation load bearing [Section III.A.1, after Eq. (50)]
    "As shown in Refs. [15–18], even in the model given by the modified action S_GRϕχ+S_λ, λ_ϕ=λ_χ=0 consistently appear as a solution. This tells that any solution of Eqs. (45) and (46) corresponding to the original action (44) is a solution for the modified model given by the action S_GRϕχ+S_λ."

    The key step that keeps the reconstructed NMO metric a solution after Lagrange-multiplier constraints are added is not proved here; it is imported from four prior papers by the same authors. The stability/no-ghost claims ('any assumed solution becomes stable') likewise rest on the authors' earlier work ([14]). This is load-bearing for the modified-gravity route, though it does not support the independent §II standard-gravity mechanism.

full rationale

The central standard-gravity claim of §II is not circular: it computes a displaced-fluid mass on a Schwarzschild background (Eqs. (8)-(17)) and then attempts a back-reacted TOV derivation (Eqs. (27)-(42)); the parameters ρ0 and w are free, not fitted to the target negative mass. That derivation does contain an independent algebraic error—combining (39) and (41) gives m ∼ 2π(1+w)/(1+3w)(Λ/κ²)r³, which is positive for −1<w<−1/3, not negative for w<−2/3 as claimed in (42)—but an incorrect derivation is a correctness risk, not a circularity. The modified-gravity sections are explicit reconstructions: the action is solved from the desired metric, so the NMO is a solution by construction, and the paper labels it 'just a formal solution'. The Lagrange-multiplier stability/no-ghost machinery is imported from self-citations ([14], [15-18]) and is load-bearing for that supporting route. Overall the central standard-gravity argument retains independent content, so the circularity score is moderate rather than high.

Axiom & Free-Parameter Ledger

7 free parameters · 6 axioms · 3 invented entities

The paper's central existence claim depends on several hand-chosen parameters (Λ < 0, ρ0, w, the ad hoc EoS (13), t0, λ, γ) and on assumptions about stability and equivalence that are inherited from previous self-cited work rather than proved here.

free parameters (7)
  • negative cosmological constant Λ = negative, unspecified
    Required input for the fluid mechanism in Section II; no numerical value or observational justification given; the sign is essential for the construction.
  • fluid density at infinity ρ0 = must satisfy 32πM²ρ0 > 1 for negative total mass (Eq. 16); §VII requires ρ0 ≳ 10^18 kg/m³ for solar mass
    Ad hoc threshold chosen to make M_total negative; not derived from independent physics.
  • equation-of-state parameter w = claimed range -1 < w < -2/3 in the asymptotic TOV analysis
    Free parameter of the perfect fluid; the negative-mass conclusion in §II.B depends on this range (and on Eq. (42), which is algebraically inconsistent with Eqs. (39)+(41)).
  • ad hoc EoS coefficients in Eq. (13) = 4/3, -6/5, 4/7, -1/9, ρ0
    Constructed by hand so that M_lost becomes finite and computable; no physical derivation.
  • time scale t0 in dynamical model (56) = positive constant, unspecified
    Sets the rate of NMO creation in Eqs. (56)-(59); chosen freely.
  • regularization scale λ in metric (55) = unspecified
    Hayward-style regulator making the negative-mass metric regular; introduced ad hoc into Eq. (55).
  • parameter γ and scale M in vanishing-mass metric (112) = γ > 1 for horizon; M arbitrary
    Controls horizon, photon sphere and shadow in Section VIII; no physical origin given.
axioms (6)
  • standard math Standard Einstein equations and TOV equations govern the fluid/geometry system (§II.B, Eqs. 27-30).
    Unproved background assumed as usual.
  • domain assumption Perfect fluid with EoS p = wρ with 0 > w > -1 can coexist with a negative cosmological constant (§II).
    Phenomenological assumption; not derived from microphysics.
  • ad hoc to paper Lagrange-multiplier constraints (50) and (73) eliminate ghosts and freeze scalar fields, making any reconstructed solution stable (§III).
    Taken from self-cited Refs. [13-18]; no stability analysis for the NMO metric itself is given.
  • domain assumption Equivalence principle m_inertia = m_gravity holds for negative-mass objects (§V, Eqs. 98-99).
    Central to the bound-state conclusion but assumed without independent support.
  • domain assumption Newtonian mechanics and Newton's law of gravity with negative masses are valid for the two-body analysis (§VI).
    The paper explicitly works in the Newtonian approximation; relativistic corrections are not controlled.
  • ad hoc to paper Any solution of Einstein's gravity is also a solution of the reconstructed model (Ref. [18]), used to argue multi-NMO configurations (§III.A.2).
    Self-cited; carried over without independent proof in this paper.
invented entities (3)
  • Negative-mass object (NMO) no independent evidence
    purpose: To produce effective anti-gravity, gravitational concave lensing, mass screening, and bound systems with positive-mass objects.
    No observed signature or fixed mass prediction; the paper gives only a conjecture about possible masses and qualitative lensing.
  • Vanishing-mass object (massless black hole) no independent evidence
    purpose: To illustrate an exotic object with zero ADM mass but a photon shadow.
    Metric in Eq. (112) is a toy model; parameters γ and M are free, and no formation mechanism or independent observable is provided.
  • Lagrange-multiplier fields λ_ϕ, λ_χ (and λ_χ in sEGB) no independent evidence
    purpose: To impose constraints that freeze scalar fields and remove ghosts in reconstructed models.
    Auxiliary fields introduced formally in Eq. (49)/(72); no physical effects outside the construction.

pith-pipeline@v1.3.0-alltime-deepseek · 18574 in / 29581 out tokens · 234306 ms · 2026-08-02T23:45:53.375289+00:00 · methodology

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read the original abstract

We conjecture the possibility of negative mass objects (NMOs) existing in the sky. It is shown that they may not be so exotic as usually expected. We show that NMOs appear as solutions of standard gravitational equations if we consider the system of a compact positive mass object, cosmological fluid and negative cosmological constant. We also construct models which generate such NMOs as solutions within the two-scalar theory and scalar-Einstein-Gauss-Bonnet gravity inspired by string theory. The orbits of the photon and massive particles are investigated in the background, where there is a negative mass object which realises a kind of effective anti-gravity. It is explicitly found that the bound system consisting of a positive mass object and a negative mass object can be formed in spite that a positive mass object suffers the repulsive force from the NMO. The possibility that such exotic objects might be observed is discussed. A simple conjecture about their possible masses is made, too. As an even more exotic object, we consider a non-trivial object with vanishing mass and investigate its properties.

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Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Observational signatures of negative mass wormholes through their shadows

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  2. Observational signatures of negative mass wormholes through their shadows

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    Numerical simulations of negative mass wormholes reveal distinct photon ring substructures in their shadows compared to Schwarzschild black holes and Simpson-Visser wormholes.

  3. Unique Gravitational-Wave Signals from Negative-Mass Binaries

    gr-qc 2026-05 unverdicted novelty 4.0

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Reference graph

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