Pith Number

pith:4D445YVM

pith:2026:4D445YVMXD4EI3QPDWYGBL6QMS

not attested not anchored not stored refs resolved

No-go theorem for spontaneous vectorization

Aofei Sang, Hsu-Wen Chiang, Sebastian Garcia-Saenz

Spontaneous vectorization cannot occur on hairless black holes without ghost or gradient instabilities

arxiv:2605.13920 v1 · 2026-05-13 · gr-qc

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\usepackage{pith}
\pithnumber{4D445YVMXD4EI3QPDWYGBL6QMS}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We demonstrate that this is not possible if the initial state is a hairless black hole, a result that applies to essentially all stationary and axisymmetric solutions of interest in general relativity. More precisely, we prove that the appearance of a negative effective mass squared for the vector field must necessarily be accompanied by ghost- or gradient-type instabilities.

C2weakest assumption

The spacetime is stationary and axisymmetric with an initial hairless black hole background, as stated for solutions of interest in general relativity.

C3one line summary

A no-go theorem shows that negative effective mass squared for the vector field in vector-tensor gravity always accompanies ghost or gradient instabilities, blocking spontaneous vectorization in stationary axisymmetric black holes.

References

74 extracted · 74 resolved · 35 Pith anchors

[1] J. D. Bekenstein, Nonexistence of baryon number for static black holes, Phys. Rev. D5, 1239 (1972) 1972

[2] J. D. Bekenstein, Nonexistence of baryon number for black holes. ii, Phys. Rev. D5, 2403 (1972) 1972

[3] J. D. Bekenstein, Novel ‘‘no-scalar-hair’’ theorem for black holes, Phys. Rev. D51, R6608 (1995) 1995

[4] Black holes in scalar-tensor gravity 2012 · arXiv:1109.6324

[5] Black hole hair in generalized scalar-tensor gravity 2014 · arXiv:1312.3622

Receipt and verification

First computed	2026-05-17T23:39:15.585083Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0f9cee2acb8f8446e0f1db060afd06492e8557f7f3a7a538eac2ef88ee77de0

Aliases

arxiv: 2605.13920 · arxiv_version: 2605.13920v1 · doi: 10.48550/arxiv.2605.13920 · pith_short_12: 4D445YVMXD4E · pith_short_16: 4D445YVMXD4EI3QP · pith_short_8: 4D445YVM

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4D445YVMXD4EI3QPDWYGBL6QMS \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e0f9cee2acb8f8446e0f1db060afd06492e8557f7f3a7a538eac2ef88ee77de0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db7d7be732b7b11a4de5654b5a00bfd5d35510edd883963d86a9da4a1c4d1927",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-05-13T13:58:10Z",
    "title_canon_sha256": "c38f60a5339dcb9f88eb73a72b5417d8ad818b46a69b39927af91c770c05aa2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13920",
    "kind": "arxiv",
    "version": 1
  }
}