Pith Number

pith:KFDGCJVZ

pith:2025:KFDGCJVZUVQPW73XZKCRBE5OIY

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Black hole thermodynamics is around the corner

Gerui Chen, Hongbao Zhang, Wei Guo, Wei Zhang, Xin Lan

A corner in the Euclidean black hole geometry yields the Wald entropy formula for generic F(R_abcd) gravity and derives the ADM Hamiltonian as conjugate to inverse temperature.

arxiv:2510.04499 v2 · 2025-10-06 · hep-th · gr-qc

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Claims

C1strongest claim

We find that the Wald formula for black hole entropy can be readily obtained for generic F(R_abcd) gravity by using both the action without the corner term and the action with the corner term due to their equivalence to the first order variation. With such an equivalence, we further make use of a special diffeomorphism to accomplish a direct derivation of the ADM Hamiltonian conjugate to the Killing vector field normal to the horizon in the Lorentz signature as a conjugate variable of the inverse temperature in the grand canonical ensemble.

C2weakest assumption

The equivalence between the action without the corner term and the action with the corner term at the level of first-order variation, which is invoked to obtain the Wald formula readily for generic F(R_abcd) gravity. This premise enters directly in the abstract as the basis for both the entropy derivation and the subsequent Hamiltonian result.

C3one line summary

A corner in the Euclidean black hole geometry enables direct derivation of the Wald entropy formula in F(R_abcd) gravity and the ADM Hamiltonian conjugate to the horizon Killing vector as the conjugate variable to inverse temperature.

References

26 extracted · 26 resolved · 0 Pith anchors

[1] J. M. Bardeen, B. Carter, and S. W. Hawking, Commun. Math. Phys.31, 161 (1973) 1973

[2] S. W. Hawking, Commun. Math. Phys.43, 199 (1975) 1975

[3] J. D. Bekenstein, Phys. Rev. D7, 2333 (1973) 1973

[4] J. B. Hartle and S. W. Hawking, Phys. Rev. D13, 2188 (1976). – 10 – 1976

[5] G. W. Gibbons and S. W. Hawking, Phys. Rev. D15, 2752 (1976) 1976

Formal links

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Receipt and verification

First computed	2026-06-08T01:03:49.157883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51466126b9a560fb7f77ca851093ae46023340ca368c5b4b8f428cb38f79fc2a

Aliases

arxiv: 2510.04499 · arxiv_version: 2510.04499v2 · doi: 10.48550/arxiv.2510.04499 · pith_short_12: KFDGCJVZUVQP · pith_short_16: KFDGCJVZUVQPW73X · pith_short_8: KFDGCJVZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KFDGCJVZUVQPW73XZKCRBE5OIY \
  | 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: 51466126b9a560fb7f77ca851093ae46023340ca368c5b4b8f428cb38f79fc2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "129dca824362a029c95ea61b156dcc0286ec621aaa4818eb5615c81e94ffe78c",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2025-10-06T05:25:13Z",
    "title_canon_sha256": "9bc3ee80037401f8793cc4cd1a22f376dd41575d5ea465ed941bd617681aa09b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.04499",
    "kind": "arxiv",
    "version": 2
  }
}