Pith Number

pith:BNV7LVIS

pith:2026:BNV7LVISCF2L6PCKU66GSTLVW6

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Thermodynamics, Phase Transitions, and Geodesic Structure of F(R)-Phantom Banados-Teitelboim-Zanelli (BTZ) Black Holes

Behzad Eslam Panah, Bilel Hamil, Manuel E. Rodrigues

F(R) phantom BTZ black holes confirm second-order phase transitions via Ehrenfest relations and support stable orbits in phantom regimes.

arxiv:2604.05646 v2 · 2026-04-07 · gr-qc · hep-th

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\usepackage{pith}
\pithnumber{BNV7LVISCF2L6PCKU66GSTLVW6}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

Our results demonstrate adherence to both Ehrenfest relations, thereby confirming the occurrence of a second-order phase transition within the black hole system concurrent with the critical point. The analysis demonstrates that stable timelike circular orbits exist only in the phantom regime for negative curvature backgrounds, while the phantom configuration also allows for stable circular photon orbits.

C2weakest assumption

The specific choice of F(R) function and the power-Maxwell nonlinear electrodynamics with phantom sign flip produce physically consistent solutions that satisfy the first law and Ehrenfest equations without unaccounted instabilities or violations of energy conditions.

C3one line summary

F(R)-phantom BTZ black holes satisfy the first law, undergo second-order phase transitions confirmed by Ehrenfest relations, and support stable circular orbits for massive and massless particles only in the phantom regime with negative curvature.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-28T01:04:39.563877Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b6bf5d5121174bf3c4aa7bc694d75b798cabb061f099e4f311a502b0e159726

Aliases

arxiv: 2604.05646 · arxiv_version: 2604.05646v2 · doi: 10.48550/arxiv.2604.05646 · pith_short_12: BNV7LVISCF2L · pith_short_16: BNV7LVISCF2L6PCK · pith_short_8: BNV7LVIS

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BNV7LVISCF2L6PCKU66GSTLVW6 \
  | 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: 0b6bf5d5121174bf3c4aa7bc694d75b798cabb061f099e4f311a502b0e159726

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "659eb06e8b1da9a887112b7b6493106c02305e25ced4f4c3a35c34de8bfb38b1",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-04-07T09:50:15Z",
    "title_canon_sha256": "573c5d07d271cefbfc99d9fc8b833e21ecdbde7d5eb61d408b88fe1bb0a9b50b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.05646",
    "kind": "arxiv",
    "version": 2
  }
}