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Rotating Topological Stars

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Pith's one-line read Rotating Topological Stars are smooth, horizonless, ergoregion-free five-dimensional solitons obtained by analytic continuation of known rotating black string solutions, with separable geodesic and scalar perturbation equations.

desk verdict A credible first rotating generalization of topological stars, with a real but likely fixable gap in the no-CTC proof. read the letter →

arxiv 2504.12235 v2 pith:HWUFRGHW submitted 2025-04-16 hep-th

Massimo Bianchi , Giuseppe Dibitetto , Jose F. Morales , Alejandro Ruipérez This is my paper · ORCID
classification hep-th
keywords angulardiscusspropagationrotatingsmoothtermstopologicaltype
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

Black holes are predicted by general relativity, but their interiors hide singularities where physics breaks down. One leading idea, the fuzzball proposal, is that what looks like a black hole from afar is actually a smooth, horizonless ball of string-theory structure. In five dimensions, the simplest such objects are 'topological stars': static, horizonless solutions supported by magnetic flux. This paper constructs rotating versions of these stars.

The authors start with a known three-parameter family of rotating black-string solutions in five-dimensional supergravity, then analytically continue one parameter so that the square of the rotation becomes negative. In this new branch, the singularity is replaced by a smooth cap where the geometry ends. To make the cap perfectly regular, the angular momentum must be quantized, and the space at infinity becomes a finite quotient of flat space. They then verify that the time Killing vector is everywhere timelike, so no ergoregion exists, and argue that closed timelike curves are absent.

Finally, they show that particles moving on geodesics have a hidden conserved quantity, making the motion integrable, and that scalar waves separate into two ordinary differential equations of confluent Heun type, the same family of equations that appears in Kerr perturbation theory. This opens the door to computing quasinormal modes and echoes that could, in principle, distinguish these objects from black holes in gravitational-wave data.

Extended reading notes

Core claim

Quote from the abstract: "We show that for specific choices of the parameters and quantized values of the angular momentum the geometry terminates on a smooth five-dimensional cap, and it displays neither ergoregion nor closed timelike curves." If true, there exists a three-parameter family of smooth, horizonless rotating solutions of minimal 5D supergravity that interpolate between Kerr and static Topological Stars, with integrable geodesic motion and scalar perturbations separating into confluent Heun equations.

Load-bearing premise

The proof of absence of closed timelike curves in Section 3.3 (after eq. (3.50)) relies on the assertion that the unshown functions D^(0)(r), D^(1)(r), G^(0)(r), G^(1)(r), G^(2)(r) are everywhere positive except at the fixed points of the isometry B_yhat. The explicit forms are not displayed, so the reader cannot verify the positivity claim that underpins the 'no CTC' conclusion. If any of these functions changed sign inside the geometry, closed timelike curves could appear and the central claim would fail.

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Referee Report

1 major / 5 minor

Summary. The paper constructs 'Rotating Topological Stars' (RTS) as a three-parameter family of solutions of five-dimensional minimal supergravity with Chern-Simons term, obtained by analytic continuation of the Compere-de Buyl-Jamsin-Virmani rotating black string to the branch a^2<0. In the regime r_b>r_s, and upon imposing the smooth-cap condition R_y=γ and the angular-momentum quantization (3.41), the solution is claimed to be horizonless, free of ergoregions and closed timelike curves, and to end on a smooth cap of topology R×S^2 while asymptoting to (R^{1,3}×S^1)/Z_q. The paper also computes five- and four-dimensional charges, discusses M-theory and type IIB embeddings in terms of brane intersections, proves separability of geodesic motion and of massless scalar perturbations, and connects the resulting confluent Heun equations to Seiberg-Witten curves.

Significance. If the unproved positivity assertion in Sec. 3.3 is confirmed, the paper delivers an explicit, horizonless, rotating soliton family in a minimal supergravity theory, continuously connected to Kerr (at r_b=0) and to the static topological star (at a=0), with integrable geodesic motion and separable scalar perturbations. This is a valuable step for the fuzzball/ECO program because the explicit metric makes concrete gravitational-wave phenomenology possible. Strengths of the presentation include the use of an independently constructed metric from [28] (so the smoothness and quantization conditions are derived rather than fitted), explicit analytic computations of charges and conserved quantities, and falsifiable predictions such as the absence of an ergoregion and the small-rotation light-ring behavior. The central no-CTC claim, however, currently rests on an unverified symbolic assertion, so the manuscript is not yet self-contained.

major comments (1)
  1. [Sec. 3.3, Eqs. (3.49)-(3.50)] The proof of absence of closed timelike curves is incomplete. The positivity of D and g_haty_haty is reduced to the assertion that the five functions D^(0), D^(1), G^(0), G^(1), G^(2) are positive except at the fixed points of B_haty, but their explicit expressions are not displayed and no proof is supplied. Since a sign change in any of these functions inside r≥r_+, |χ|<1 would make the determinant or g_haty_haty negative and would create CTCs, this is a load-bearing gap in the abstract's central claim. Please provide the explicit rational forms, in an appendix if necessary, together with a verification of positivity over the full domain of parameters and coordinates; as the functions are rational in r and χ, this is a finite check that can be documented.
minor comments (5)
  1. [Eq. (3.46)] The inequality chain is not valid as written: from r≥r_+>r_b and 0<ξ_t<1 one cannot conclude ((1-ξ_t^2)r-r_b)/r>0, since r_+ may be smaller than r_b/(1-ξ_t^2); for example r_s=0.9, r_b=1, r_+=1.1 gives a negative value at r=r_+. The no-ergoregion conclusion nevertheless follows immediately from (3.45), where rb>rs makes all displayed terms nonnegative, so the faulty intermediate step should be corrected or deleted.
  2. [Sec. 3.1 and Eq. (3.30)] The phase-diagram paragraph refers to 'section ??' for a detailed discussion, and the text after Eq. (3.30) contains an unresolved '[?]' citation; both should be completed.
  3. [Fig. 1 caption] The caption uses t1 and t2 without defining these quantities in the text, so the reader cannot tell which projected line corresponds to which phase.
  4. [Sec. 4, Eq. (4.33)] The exact light-ring condition for general rotation is stated to be a quintic, but the small-a expansion (4.34) is carried only to first order; the text should state explicitly that existence and uniqueness of light rings for arbitrary a is left open.
  5. [Abstract] The phrase 'smooth five-dimensional cap' could be misread: the cap itself has topology R×S^2 and is a three-dimensional locus at which the y-circle shrinks; consider rephrasing to 'the five-dimensional geometry ends on a smooth cap'.
Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The solution parameters r_s, r_b and h/q label the geometry and are fixed by boundary data (mass and compactification radius); they are not fitted to any target result. No ad hoc constants are introduced. The paper relies on the cited prior solution [28] as an external benchmark, and on the unshown positivity of the CTC-related functions, which is the main ad hoc input. No new particles or forces are introduced.

assumptions (5)
  • domain assumption The known G2-dual solution of Compere et al. (Eq. 3.4) solves the minimal 5D supergravity action (3.1).
    The construction starts from this solution, taken from [28]; the paper does not re-derive it.
  • domain assumption Analytic continuation to imaginary a^2 preserves the field equations and yields a real Lorentzian metric via the symmetry (3.6).
    The paper states the continuation is valid but does not prove it in detail; it is a standard property of the parameterization.
  • ad hoc to paper All undisplayed functions D^(0), D^(1), G^(0), G^(1), G^(2) in eqs. (3.49)-(3.50) are positive except at fixed points of B_yhat.
    This is asserted without explicit expressions and is needed to exclude closed timelike curves, a load-bearing element of the central claim.
  • domain assumption The asymptotic orbifold (R^{1,3} x S^1)/Z_q with the stated action (3.38) is an admissible boundary condition.
    The paper uses this quotient to make the would-be twisted identifications consistent; it changes the asymptotic falloff in a controlled way.
  • domain assumption Equal-charge identification Q1=Q2=Q3 in brane systems gives the static TS limit and the stringy embeddings.
    Used in Section 2 to connect the solution to M5-brane and KK-D1-D5 systems; this is an identification of parameters, not a derivation of the 5D action.

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Pith. "Pith review of Rotating Topological Stars." pith.science (2026). https://pith.science/paper/HWUFRGHW

@misc{pith2026250412235,
  author       = {Pith},
  title        = {Pith review of: Rotating Topological Stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HWUFRGHW}},
  note         = {Machine review of arXiv:2504.12235}
}
read the original abstract

We construct a three-parameter family of smooth and horizonless rotating solutions of Einstein-Maxwell theory with Chern-Simons term in five dimensions and discuss their stringy origin in terms of three-charge brane systems in Type IIB and M-theory. The general solution interpolates smoothly between Kerr and static Topological Star geometries. We show that for specific choices of the parameters and quantized values of the angular momentum the geometry terminates on a smooth five-dimensional cap, and it displays neither ergoregion nor closed timelike curves. We discuss the propagation of particles and waves showing that geodetic motion is integrable and the radial and angular propagation of scalar perturbations can be separated and described in terms of two ordinary differential equations of confluent Heun type.

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Forward citations

Cited by 5 Pith papers

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

  1. 5d Schwarzschild-Tangherlini spacetime: MST-like formalism for a Reduced Confluent Heun Equation

    gr-qc 2026-07 conditional novelty 7.0 of 10

    An original MST-like formalism is constructed for the reduced confluent Heun radial equation of 5D Schwarzschild-Tangherlini scalars, validated by matching the renormalized angular momentum to the quantum Seiberg-Witt...

  2. "Waveforms" at the Horizon

    gr-qc 2026-02 conditional novelty 6.0 of 10

    A probe scattering off a Schwarzschild black hole transfers a definite leading-order post-Minkowskian angular momentum to the horizon, given by new closed formulas (3.24b), (3.29), (3.36).

  3. Characterizing geodesic deviations in a Topological Star spacetime: massive, charged, spinning and stringy-like objects

    gr-qc 2025-05 conditional novelty 6.0 of 10

    Nearby geodesics, spinning particles, magnetically charged particles and string probes all deviate from geodesic motion in a topological star, reducing to Schwarzschild plus small alpha-dependent corrections.

  4. Probing the multipolar structure of Myers-Perry black holes with scattering amplitudes

    hep-th 2025-05 conditional novelty 6.0 of 10

    A Kerr-Schild gauge computation gives analytic scattering amplitudes and eikonal phases for Myers-Perry black holes, exposing spin-induced stress multipoles that have no four-dimensional counterpart.

  5. Extreme mass ratio inspirals around topological stars

    gr-qc 2025-04 conditional novelty 6.0 of 10

    A scalar charge orbiting a topological star produces fluxes that deviate from the black hole case and can dephase by up to 10^4 radians over a year, while QNM resonances are too narrow to be observable.

Reference graph

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