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arxiv: 2411.12413 · v3 · pith:5SLOY553new · submitted 2024-11-19 · ✦ hep-th · gr-qc

Attractor saddle for 5D black hole index

Soumya Adhikari , Pavan Dharanipragada , Kaberi Goswami , Amitabh Virmani This is my paper

Pith reviewed 2026-05-23 08:38 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords saddlesolutionblackformholeindexsupersymmetricanupam
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The pith

The non-extremal saddle for the 5D BMPV black hole index is expressed in canonical harmonic-function form on a flat base, establishing supersymmetry and the new attractor property.

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

The work takes a complex finite-temperature solution previously built by another group for the supersymmetric index of a five-dimensional black hole with three charges. That solution saturates the BPS bound in the classical limit. The authors recast the same geometry using three harmonic functions defined on ordinary flat three-dimensional space. In this language the Killing spinor equations become manifestly satisfied, proving the configuration is supersymmetric. The same rewriting also makes visible an attractor mechanism in which the scalar fields flow to fixed values at the horizon independent of their asymptotic values. Because the base is flat, the construction stays within the standard five-dimensional supergravity framework without introducing new fields or dimensions. The result therefore supplies an explicit, checkable representative of the saddle that contributes to the black-hole index.

Core claim

We write this solution in a canonical form in terms of harmonic functions on three-dimensional flat base space, thereby showing that it is supersymmetric. We also show that it exhibits the new form of attraction.

Load-bearing premise

The solution constructed in arXiv:2308.00038 is the correct non-extremal saddle that saturates the BPS bound and reproduces the supersymmetric index in the classical limit; the present rewriting inherits all properties of that prior construction.

read the original abstract

In a recent paper, Anupam, Chowdhury, and Sen [arXiv:2308.00038] constructed the non-extremal saddle that reproduces the supersymmetric index of the BMPV black hole with three independent charges in the classical limit. This saddle solution is a finite temperature complex solution saturating the BPS bound. In this paper, we write this solution in a canonical form in terms of harmonic functions on three-dimensional flat base space, thereby showing that it is supersymmetric. We also show that it exhibits the new form of attraction.

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.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on the existence and uniqueness properties of harmonic functions on flat 3D space, the standard Killing-spinor equations of 5D N=2 supergravity, and the correctness of the saddle constructed in the referenced work. No new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • standard math Harmonic functions on flat 3D Euclidean space satisfy the Laplace equation and generate supersymmetric solutions when used as building blocks for the metric and gauge fields.
    Invoked when the solution is rewritten in canonical harmonic-function form.
  • domain assumption The non-extremal saddle of arXiv:2308.00038 saturates the BPS bound and reproduces the supersymmetric index in the classical limit.
    The present work inherits all physical properties from that prior construction.

pith-pipeline@v0.9.0 · 5625 in / 1427 out tokens · 34095 ms · 2026-05-23T08:38:02.160346+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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

  1. Non-supersymmetric F1-P black rings

    hep-th 2026-01 unverdicted novelty 7.0

    Singly and doubly spinning non-supersymmetric F1-P black ring solutions are constructed in 5D supergravity, with the doubly spinning case admitting an extremal limit where entropy S equals 2 pi times the S^2 angular m...

Reference graph

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