A local first law for black hole thermodynamics

Ernesto Frodden (1, 2) , Amit Ghosh (3) , Alejandro Perez (2)

1 Departamento de Física
2 CPT - Centre de Physique Théorique - UMR 7332
3 SINP - Saha Institute of Nuclear Physics

We first show that stationary black holes satisfy an extremely simple local form of the first law δE = κ/8π δA where the thermodynamical energy E=A/(8πl) and (local) surface gravity κ = 1/l, where A is the horizon area and l is a proper length characterizing the distance to the horizon of a preferred family of local observers suitable for thermodynamical considerations. Our construction is extended to the more general framework of isolated horizons. The local surface gravity is universal. This has important implications for semiclassical considerations of black hole physics as well as for the fundamental quantum description arising in the context of loop quantum gravity.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

Ernesto Frodden, Amit Ghosh, Alejandro Perez. A local first law for black hole thermodynamics. 2011. ⟨hal-00957643⟩