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New rotating Lorentzian wormhole spacetime

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Pith's one-line read A new rotating Lorentzian wormhole, built from the static zero-Ricci wormhole, is shown to be regular, asymptotically flat, and consistent with EHT shadow bounds.

desk verdict The rotating wormhole metric is new and seems sound, but the shadow and EHT constraints rest on a Hamilton-Jacobi separability that fails for p≠0, plus an ADM mass normalization error; the geometry deserves review, the observational section does not. read the letter →

arxiv 2411.09202 v3 pith:J5YUTKI3 submitted 2024-11-14 gr-qc hep-th

Anjan Kar , Soumya Jana , Sayan Kar This is my paper · ORCID
classification gr-qchep-th MSC 83C1583C2083C57
keywords rotatingwormholeLorentzianNewman-JanisalgorithmAzreg-AinoumethodshadowenergyconditionsKerr-likespacetimezeroRicciscalar
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that the static, spherically symmetric zero-Ricci wormhole has a rotating counterpart, and that the new line element is a genuine wormhole rather than a disguised black hole. It argues that the Newman-Janis algorithm and its generalized version fail for this seed, while the Azreg-Ainou method succeeds and yields an explicit metric with three parameters: mass $M$, rotation $a$, and a dimensionless $p$. The authors show the metric reduces to the known static wormhole at $a=0$, to Kerr at $p=0$, has a throat at $r=2M$, no horizon or ergosphere, and finite curvature invariants on and outside the throat. They then compute the shadow and find it compatible with M87* and SgrA* observations, with the SgrA* fractional deviation bound selecting $p\leq0.24$. A sympathetic reader would care because this gives a concrete, observationally testable wormhole that mimics Kerr at large distances and sharpens the black-hole-mimicker program.

What carries the argument

The load-bearing mechanism is the Azreg-Ainou procedure: rather than complexifying the radial coordinate as in the Newman-Janis method, it promotes the seed functions $f(r),g(r),h(r)$ to three-variable functions $A,B,\Psi$, fixes them by requiring the Boyer-Lindquist components $g_{tr}=g_{r\phi}=0$, and then solves the constraint $G_{r\theta}=0$. The crucial step is the solution $\Psi=K+a^2\cos^2\theta$, where $K(r)=h\sqrt{g/f}$; this choice is what converts the static seed into the explicit metric (3.33). The Hamilton-Jacobi equation for null geodesics is separable for this Kerr-like form, which is what makes the shadow computation possible.

What would settle it

Solve Eq. (3.28) for $\Psi$ without imposing Eq. (3.29) and check for other regular solutions that reduce to $h(r)$ as $a\to0$ and satisfy the wormhole conditions; if any exist, the metric (3.33) is not the uniquely determined rotating counterpart. A cleaner settle would be an independent derivation of the same metric from a specified axisymmetric matter source in an explicit gravity theory.

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Extended reading notes

Core claim

The central discovery is the line element (3.33), with $\Sigma = r^2 + a^2\cos^2\theta$, $m(r)$ as in (3.34), and $\Delta(r)$ as in (3.35). In the $a\to0$ limit it returns the static $R=0$ wormhole, in the $p\to0$ limit it returns Kerr, and for $a\neq0$, $p\neq0$ it is a Kerr-like rotating wormhole: the throat sits at $r=2M$ with throat radius $S|_{r=2M} = [4M^2 + a^2(p^2+4p+2)/(p+1)^2]^{1/2}$, the spacetime is asymptotically flat, and the six independent Zakhary-McIntosh curvature invariants are finite and smooth on $r\in[2M,\infty)$. The metric has no ergosphere because $g_{tt}<0$ everywhere, it is not of Teo type but belongs to the Damour-Solodukhin-inspired Kerr-like class, and the matter required in general relativity violates all energy conditions, as expected for a wormhole. The null Hamilton-Jacobi equation separates, giving an analytic shadow; the shadow satisfies the EHT circularity bound for all allowed parameters and satisfies the SgrA* fractional-deviation bound only for $p\lesssim0.24$.

Load-bearing premise

The whole construction depends on an assumed shortcut for how the metric functions depend on angle under rotation, namely $\Psi=K+a^2\cos^2\theta$; the paper does not prove that this shortcut is the unique one that the physics requires, so if it is wrong the new metric is just one of many hand-built rotating spacetimes rather than the rotating version of the original wormhole.

Editorial extensions

If this is right

  • The $R=0$ static wormhole now has an explicit rotating extension, and the obstruction that blocked the Newman-Janis route is understood: the transformation functions $\chi_1,\chi_2$ become $\theta$-dependent.
  • The spacetime is a black-hole mimicker: it approaches Kerr asymptotically and its shadow for $p\lesssim0.24$ is consistent with SgrA* and M87* data, so current observations cannot exclude it.
  • Because $\Delta(r)$ has no zero on $r\ge2M$ and $g_{tt}<0$ everywhere, there is no horizon and no ergosphere; this gives concrete differences from Kerr in photon orbits, lensing, and accretion signatures near the throat.
  • The energy-condition violation, while expected, is severe in GR; any physical realization must live in an alternative theory such as braneworld gravity, where the effective geometric stress may satisfy the null energy condition.
  • The SgrA* bound $p\le0.24$ is a sharp prediction: future measurements of shadow fractional deviation outside this range would eliminate the wormhole as a model for SgrA*.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension the authors leave open is to derive (3.33) from a specific axisymmetric scalar-field solution in the braneworld; if that succeeds, the GR energy-condition violation would be reinterpreted as geometric stress, and the rotating wormhole would gain a dynamical field-theoretic status.
  • The success of $\Psi=K+a^2\cos^2\theta$ suggests testing whether the Azreg-Ainou method with this ansatz generates Kerr-like rotating families for other static seeds whose Newman-Janis transform is obstructed; uniqueness of the ansatz is not established, so each such construction needs independent verification.
  • The shadow analysis assumes the standard wormhole-shadow convention: all light sources are on the observer's side and the other mouth is dark. If sources exist inside the far mouth or near the throat, the observable image could differ qualitatively from the dark spot computed here.
  • The $p\le0.24$ bound is testable with next-generation very-long-baseline interferometry; a measured $\delta$ outside that interval for SgrA* would single out Kerr-like models and rule out this specific wormhole.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper applies the Azreg-Ainou algorithm to the static R=0 wormhole of Eq. (2.5) and obtains a new rotating, asymptotically flat, axially symmetric line element, Eq. (3.33), with mass function m(r) in Eq. (3.34) and radial function Δ(r) in Eq. (3.35). The authors argue that this metric reduces to the static R=0 wormhole for a=0 and to Kerr for p=0, that it has a throat at r=2M with regular curvature invariants on the wormhole domain, that the supporting matter in GR violates the energy conditions, and that the spacetime possesses no ergosphere. They then compute shadow profiles under an assumed Hamilton-Jacobi separability and compare them with EHT observations of M87* and SgrA*, deriving a bound p≲0.24 from the fractional deviation parameter δ.

Significance. If sound, the paper gives an explicit, regular rotating wormhole that interpolates between Kerr and a known static wormhole, with concrete observables (shadow, energy-condition violations) that could be tested against black-hole-shadow data. The geometric construction is largely self-contained: the limits p=0 and a=0 are correctly identified, the throat condition and embedding diagrams support the wormhole interpretation, and the displayed curvature invariants are finite on r≥2M. However, the observational part rests on two load-bearing assumptions: exact Hamilton-Jacobi separability of the null geodesic equation and the identification of M as the ADM mass. Both need to be established or corrected before the EHT comparison can be trusted.

major comments (2)
  1. [§V, Eqs. (5.5)–(5.10)] The Hamilton-Jacobi separability of the metric (3.33) is asserted but not demonstrated, and the assertion is questionable. For the inverse metric, the g^{rr} component is Δ/Σ with Δ given by Eq. (3.35), while the t-φ sector contains the different combination Δ_std = r² − 2m(r)r + a². For p ≠ 0 these two quantities are not equal; for example, with M=1, p=0.5, a=0.5, r=3 one finds Δ≈3.16 while Δ_std≈4.89. The standard Kerr-like separable form requires the same Δ to appear in the radial and in the t-φ block. The paragraph after Eq. (5.8) merely claims that the construction of Refs. [71–73] applies and that the metric 'belongs to the same general class', without verifying the X^{ij}, Y^{ij} constraints for this specific Δ(r). Unless explicit verification is provided, the separated angular and radial equations (5.4)–(5.6), the critical parameters (5.10), and all shadow profiles and EHT bounds in §V B are unsupported. The authors should either prove separability for the line element (3.33) or remove the shadow/EHT section and temper the corresponding conclusions.
  2. [§III C, Eq. (3.34); §V B; §VI] The parameter M is not the ADM mass of the spacetime. From Eq. (3.34), m(r) → M/(p+1) as r → ∞, so the asymptotic form of gtt is −1 + 2M/((p+1)r) + O(r⁻²). The correct ADM mass is therefore M_adm = M/(p+1), not M. The paper nevertheless calls M the ADM mass throughout, for example in the concluding paragraph of §VI, and uses M as the normalization scale in the shadow plots and in the fractional deviation parameter δ of Eq. (5.15). Since δ compares the shadow diameter with 3√3 M_adm, using M instead of M/(p+1) rescales δ by a factor (p+1) and changes the exclusion plot in Fig. 13 (right) and the stated bound p≲0.24. The mass interpretation must be corrected, or the EHT constraints must be recomputed using the actual ADM mass.
minor comments (5)
  1. [§III B, Eq. (3.29)] The choice Ψ = K + a² cos²θ is presented as a solution of the G_{rθ}=0 constraint, but the paper does not address whether the Azreg-Ainou construction with this Ψ is unique or whether other choices would change the resulting rotating geometry. A sentence acknowledging this limitation would help calibrate the claim that Eq. (3.33) is the rotating counterpart of the static wormhole.
  2. [§IV A, after Eq. (4.8)] The wormhole criteria are stated but the flare-out condition ∂b/∂r < 0 at the throat is not explicitly checked with the numerical or analytic expressions; the authors say 'one can easily verify' without showing the calculation. This is a short addition that would make the wormhole claim easier to check.
  3. [§V B, Fig. 13 caption and text] The text says ΔC reaches a maximum value of 0.005 for p=0, a=0.99, while the colorbar in Fig. 13 (left) appears to saturate at 0.004. Please make the value consistent.
  4. [General] The allowed domain of the parameter p is never stated explicitly. The metric and plots appear to assume p ≥ 0, and the discussion mentions extending p > 1.5; this should be stated and justified (e.g., for positivity of N² and regularity of the wormhole).
  5. [§V, Eq. (5.11)] The celestial coordinates α and β are defined with a finite observer distance r0, but the shadow formulas (5.12) are taken in the limit r → ∞. The notation should make clear that the observer is asymptotically far, and the limit should be stated consistently.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the rotating metric is an explicit construction and the shadow analysis is a genuine calculation followed by an observational constraint.

full rationale

The derivation chain is self-contained: Eq. (3.33) with m(r) and Delta(r) from Eqs. (3.34)-(3.35) is an explicit output of the Azreg-Ainou algorithm, and the stated limits a->0 (static R=0 seed) and p->0 (Kerr) are direct algebraic substitutions into those formulas, not fitted predictions. The wormhole checks (throat at r=2M, flare-out, no ergosphere, finite ZM invariants) are computed from the explicit metric and are falsifiable in principle. In Section V the shadow is obtained from a Hamilton-Jacobi separation that is asserted by appeal to refs. [71-73] without verification of the X^{ij}, Y^{ij} constraints; that is a rigor/correctness gap, but not a circularity, because the shadow is not fitted to EHT data and then re-presented as a prediction. The EHT delta bound is applied after the fact to constrain p, so no fitted parameter is renamed as a prediction. Self-citations occur (e.g., [37], [39], [84]), but the static seed is rederived in Section II and the shadow formulas are standard; none of these citations carries the load of the central construction. The admitted ansatz Psi=K+a^2 cos^2 theta in Eq. (3.29) limits the strength of the claim that this is the rotating version of the seed, but it is a stated assumption, not a circular reduction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The construction introduces no new fundamental entities; it postulates a three-parameter family of metrics and defines the supporting matter as whatever the Einstein tensor requires. The EHT comparison is an application that constrains the free parameters, not an independent source of the metric.

free parameters (3)
  • M = not fitted; parameter of the seed metric
    Mass parameter that sets the throat radius r=2M. The paper calls it ADM mass, but the asymptotic mass from Eq. (3.34) is M/(1+p).
  • a = not fitted; constrained only by EHT allowed region
    Spin parameter of the rotating wormhole; controls the shift and distortion of the shadow.
  • p = claimed p<=0.24 from SgrA* delta, but this bound depends on the flawed mass normalization
    Dimensionless deviation parameter; p=0 recovers Kerr and a=0 recovers the static R=0 wormhole.
assumptions (5)
  • standard math Einstein equations with T=G and kappa=1 define the matter source
    Used in Section IVB to compute energy density and pressures from the metric.
  • domain assumption The static R=0 wormhole in Eq. (2.5) is a valid spacetime
    Seed geometry taken from Refs. [36-39]; it is known to be non-vacuum and to violate energy conditions in GR.
  • ad hoc to paper The Azreg-Ainou ansatz with Psi=K+a^2 cos^2 theta yields the rotating extension
    Eqs. (3.28)-(3.29): the choice Psi=K+a^2 cos^2 theta is one solution of G_{r theta}=0, assumed without uniqueness or physical derivation.
  • domain assumption The null Hamilton-Jacobi equation separates for the new metric
    Section V, Eqs. (5.4)-(5.6): separability is taken from Refs. [71-73] and not proved for the specific m(r).
  • domain assumption The spacetime is Petrov type D and six ZM invariants suffice for regularity
    Section IVC: relies on Ref. [65] for the classification and on numerical plots of the invariants to infer non-singularity.

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Pith. "Pith review of New rotating Lorentzian wormhole spacetime." pith.science (2026). https://pith.science/paper/J5YUTKI3

@misc{pith2026241109202,
  author       = {Pith},
  title        = {Pith review of: New rotating Lorentzian wormhole spacetime},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J5YUTKI3}},
  note         = {Machine review of arXiv:2411.09202}
}
abstract

A rotating version of a known static, spherically symmetric, zero Ricci scalar Lorentzian wormhole is constructed. It turns out that for this given non-rotating geometry, the standard Newman-Janis algorithm does not produce a rotating wormhole and, therefore, the method pioneered by Azreg-A\"inou has to be used. The rotating spacetime thus obtained is shown to be regular with wormhole features, though it is no longer a $R=0$ spacetime. The required matter is found to violate the energy conditions, as expected. A few other characteristic properties of this new rotating spacetime are mentioned. Finally, we calculate the shadow for this geometry and discuss its features {\em vis-a-vis} the Kerr geometry and available event horizon telescope observations.

Figures

Figures reproduced from arXiv: 2411.09202 by the authors.

Figure 1
Figure 1. Embedding diagram of the rotating wormhole. [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. The variation of energy density (ρ) is shown w.r.t. r for different values of a and p at θ = π/2. a = 0.00 M a = 0.25 M a = 0.75 M a = 1.00 M 2.000 2.005 2.010 2.015 2.020 -7 -6 -5 -4 -3 -2 -1 0 r/M ρ + p1 p = 0.1 and θ = 90° a = 0.00 M a = 0.25 M a = 0.75 M a = 1.00 M 2.00 2.05 2.10 2.15 2.20 -0.8 -0.6 -0.4 -0.2 0.0 r/M ρ + p1 p = 0.5 and θ = 90° a = 0.00 M a = 0.25 M a = 0.75 M a = 1.00 M 2.00 2.05 2.10 2.15 2.20 … view at source ↗
Figure 3
Figure 3. The variation of different null energy conditions are shown w.r.t. [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: The variation of Null and Weak energy conditions (EC) at the throat is shown [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: Variation of Ricci scalar (g µνRµν) with r and θ for different sets of a and p (a) a/M = 1.0 and p = 0 (b) a/M = 0.5 and p = 0.5 (c) a/M = 0 and p = 1.0 [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]
Figure 6
Figure 6. Figure 6: Variation of RµνRµν scalar with r and θ for different sets of a and p (a) a/M = 1.0 and p = 0 (b) a/M = 0.5 and p = 0.5 (c) a/M = 0 and p = 1.0 [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: Variation of C µνλδCµνλδ scalar with r and θ for different sets of a and p p leads to a non-zero value of the Ricci scalar ( [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: Variation of the invariant I2 with r and θ for different sets of a and p (a) a/M = 1.0 and p = 0 (b) a/M = 0.5 and p = 0.5 (c) a/M = 0 and p = 1.0 [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: Variation of the invariant I9 with r and θ for different sets of a and p (a) a/M = 1.0 and p = 0 (b) a/M = 0.5 and p = 0.5 (c) a/M = 0 and p = 1.0 [PITH_FULL_IMAGE:figures/full_fig_p018_9.png]
Figure 10
Figure 10. Figure 10: Variation of the invariant I10 with r and θ for different sets of a and p other independent curvature invariants as defined in Eqs. 4.20 for the entire domain of the radial (r) and angular (θ) coordinates. One may note that when a ̸= 0 and p = 0, i.e. the Kerr metric,…
Figure 11
Figure 11. Figure 11: Shadow profiles of the rotating wormhole for different values of [PITH_FULL_IMAGE:figures/full_fig_p022_11.png]
Figure 12
Figure 12. Figure 12: Shadow profiles for different inclination angle [PITH_FULL_IMAGE:figures/full_fig_p023_12.png]
Figure 13
Figure 13. Figure 13: The contour plot for different values of ∆ [PITH_FULL_IMAGE:figures/full_fig_p025_13.png]

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