Pith Number

pith:QCYZMJZB

pith:2016:QCYZMJZBF25ZXTH6QDF7CULUEF

not attested not anchored not stored refs resolved

Black hole chemistry: thermodynamics with Lambda

David Kubiznak, Mae Teo, Robert B. Mann

Treating the cosmological constant as pressure makes black hole mass into enthalpy and reveals chemical phase transitions.

arxiv:1608.06147 v3 · 2016-08-22 · hep-th · gr-qc

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\usepackage{pith}
\pithnumber{QCYZMJZBF25ZXTH6QDF7CULUEF}

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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

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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

Black holes can be understood from the viewpoint of chemistry, in terms of concepts such as Van der Waals fluids, reentrant phase transitions, and triple points.

C2weakest assumption

The cosmological constant can be consistently interpreted as a thermodynamic pressure and the black-hole mass as chemical enthalpy, an identification that extends the first law beyond the standard fixed-Lambda formulation.

C3one line summary

Treating the cosmological constant as pressure in black hole thermodynamics yields an extended dictionary with enthalpy, thermodynamic volume, and chemical-like phase transitions including Van der Waals behavior, reentrant transitions, and triple points.

References

294 extracted · 294 resolved · 246 Pith anchors

[1] J. M. Bardeen, B. Carter and S. W. Hawking, The Four laws of black hole mechanics , Commun. Math. Phys. 31 (1973) 161–170. – 70 – 1973

[2] Israel, Event horizons in static vacuum space-times , Phys 1967

[3] J. D. Bekenstein, Black holes and entropy , Phys.Rev. D7 (1973) 2333–2346 1973

[4] S. W. Hawking, Particle Creation by Black Holes , Commun. Math. Phys. 43 (1975) 199–220 1975

[5] The black hole information paradox 1995 · arXiv:hep-th/9508151

Formal links

3 machine-checked theorem links

Cited by

21 papers in Pith

Properties of black holes in non-linear electrodynamics

A Note on Chaos in Hayward Black Holes with String Fluids

Thermal and Optical Signatures of Einstein-Dyonic ModMax Black Holes with GUP and Plasma Modifications

Holographic Extended Thermodynamics of deformed AdS-Schwarzschild black hole

Gravitational constant as a conserved charge in black hole thermodynamics

Receipt and verification

First computed	2026-05-17T23:38:14.373768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80b19627212ebb9bccfe80cbf1517421777d1856f8627b38751f822620de962e

Aliases

arxiv: 1608.06147 · arxiv_version: 1608.06147v3 · doi: 10.48550/arxiv.1608.06147 · pith_short_12: QCYZMJZBF25Z · pith_short_16: QCYZMJZBF25ZXTH6 · pith_short_8: QCYZMJZB

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/QCYZMJZBF25ZXTH6QDF7CULUEF \
  | 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: 80b19627212ebb9bccfe80cbf1517421777d1856f8627b38751f822620de962e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "402179541cd0b5727f692f201eab21201d20d270076d21293f65e9c3a92a1518",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2016-08-22T12:32:49Z",
    "title_canon_sha256": "bbaf8d49e13be1558ecba48ca510c49cc26db11f08355772ae106984e6f87990"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.06147",
    "kind": "arxiv",
    "version": 3
  }
}