inner-extremal-rbh: no attractor for degenerate inner horizons, and the NEC-satisfying family it rules out selecting

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Authors: Oleh Popenkov
Cited by: 4

Abstract

Reproduction package for the paper Inner-extremal regular black holes with NEC-satisfying anisotropic sources: existence, extent, and the absence of a classical selection mechanism. Every number in the paper is reproduced by one command from a clean clone; the map from each number to its script and result file is in docs/reproducibility.md, and the scope of every claim is in docs/limitations.md. A family of regular black holes whose inner horizon is degenerate — a triple root of the metric function, so that the surface gravity vanishes and the Cauchy-horizon instability is switched off at linear order — exists over a finite range of the core scale and satisfies the null energy condition throughout. No local matter source in general relativity selects it. Between the horizons the geometry is a homogeneous Kantowski–Sachs region whose dynamics closes on the areal radius; the phase-space divergence of that flow vanishes identically, for any metric function and any explicit time dependence, so the flow is Hamiltonian, Liouville's theorem applies, and no attractor exists. With a velocity-dependent transverse pressure the flow is no longer Hamiltonian, but the Jacobian at the degenerate horizon still has zero trace, so such a horizon is never asymptotically stable. The result concerns the unreduced symplectic dynamics at fixed profile, and no energy condition enters the proof. Version 1.1.1 adds the theorem with its symbolic proof and numerical controls (src/no_attractor/), the analysis of non-spherical perturbations (src/nonspherical/), and the phase-space area figure. Licensing is split: code in src/ and figures/ is MIT; data in data/, raw logs in logs/ and the generated figure images are CC-BY-4.0. See LICENSE. The calculations were carried out with automated agents under the author's direction, with an independent cross-audit between two separate research projects. The author is responsible for the results.

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
16 September 2026
Language
EN