Rotation overcharges vectorized black holes

Abstract

A charged black hole has a ceiling: extremality bounds the charge that a given mass and spin can support. Vector hair has so far only lowered it. In the Einstein--Maxwell--Vector (EMV) model, where a massless vector field couples nonminimally to the electromagnetic invariant, the spherically symmetric vectorized Reissner--Nordström black holes are strictly undercharged: vector hair is paid for in charge. Whether this ceiling is a property of the vector field or merely of spherical symmetry has remained open, because spherical symmetry hides the hair's mass as well: its Komar mass vanishes identically and the exact identity M_V=2Ω_HJ_V degenerates to 0=0. Rotation lifts both degeneracies at once. We construct the rotating solutions of the model, the first in this setting, and find that the hair's mass is not a free parameter but a second-order invariant of the rotational response, fixed by M_V=2Ω_HJ_V. Above a coupling threshold the ceiling gives way: the domain of existence crosses the extremal Kerr--Newman bound, reaching q=Q/M>1 with q²+χ² up to $1.84$, while at α=5 the maximum charge stays below it. The shadow is where the hair becomes visible. At (q,χ)=(0.9947,0.10), near the extremal bound, the hair contributes an ellipticity of 8.30%, against 0.44% from the charge and 0.06% from rotation --- a factor of $19$ that charging a Kerr black hole cannot mimic; at the overcharged solution (q,χ)=(1.2527,0.10) the total ellipticity reaches 25.6%. Whether the branch is ghost-free remains open, but the existing no-go criteria do not settle it: they assume a background and a dispersion relation that do not hold here.

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BibTeX RIS

BibTeX

@misc{guo2026rotation,
  title = {{Rotation overcharges vectorized black holes}},
  author = {Shengjun Guo and Guangzai Ye and Peng Liu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40179},
  eprint = {2610.40179},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40179},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Rotation overcharges vectorized black holes
AU  - Shengjun Guo
AU  - Guangzai Ye
AU  - Peng Liu
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40179
UR  - https://arxiv.org/abs/2610.40179
AB  - A charged black hole has a ceiling: extremality bounds the charge that a given mass and spin can support. Vector hair has so far only lowered it. In the Einstein--Maxwell--Vector (EMV) model, where a massless vector field couples nonminimally to the electromagnetic invariant, the spherically symmetric vectorized Reissner--Nordström black holes are strictly undercharged: vector hair is paid for in charge. Whether this ceiling is a property of the vector field or merely of spherical symmetry has remained open, because spherical symmetry hides the hair's mass as well: its Komar mass vanishes identically and the exact identity M_V=2Ω_HJ_V degenerates to 0=0. Rotation lifts both degeneracies at once. We construct the rotating solutions of the model, the first in this setting, and find that the hair's mass is not a free parameter but a second-order invariant of the rotational response, fixed by M_V=2Ω_HJ_V. Above a coupling threshold the ceiling gives way: the domain of existence crosses the extremal Kerr--Newman bound, reaching q=Q/M>1 with q^2+χ^2 up to $1.84$, while at α=5 the maximum charge stays below it. The shadow is where the hair becomes visible. At (q,χ)=(0.9947,0.10), near the extremal bound, the hair contributes an ellipticity of 8.30%, against 0.44% from the charge and 0.06% from rotation --- a factor of $19$ that charging a Kerr black hole cannot mimic; at the overcharged solution (q,χ)=(1.2527,0.10) the total ellipticity reaches 25.6%. Whether the branch is ghost-free remains open, but the existing no-go criteria do not settle it: they assume a background and a dispersion relation that do not hold here.
ER  -

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