Entanglement entropy of black holes from the first law of thermodynamics

@misc{diakonov2026entanglement,
  title = {{Entanglement entropy of black holes from the first law of thermodynamics}},
  author = {D. V. Diakonov and Gleb S. Zverev},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11777},
  eprint = {2610.11777},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11777},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Entanglement entropy of black holes from the first law of thermodynamics
AU  - D. V. Diakonov
AU  - Gleb S. Zverev
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11777
UR  - https://arxiv.org/abs/2610.11777
AB  - We compute the entanglement entropy of quantum matter in spacetimes with a Killing horizon entirely on-shell, by integrating the first law of thermodynamics along a one-parameter family of equilibrium backgrounds labelled by the Hawking temperature. This yields a closed expression in terms of the renormalized stress-energy tensor and the Killing vector, finite by construction, with no replicas and no conical singularities. Its covariant form agrees with the matter terms of the Bardeen--Carter--Hawking mass variation formula. We show in details that for static patch of de Sitter space and for the non-rotating BTZ black hole it reproduces the conical entropy exactly, contact term Q included.
ER  -