A local first law for black hole thermodynamics

2011/10/18 by Ernesto Frodden, Amit Ghosh, Frodden, Ernesto +4 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory #gr-qc #hep-th

paper · pdf · doi:10.48550/arxiv.1110.4055

The derivation of the main result for the special case of isolated horizons has been considerably strengthen

openalex publication_date 2011/10/18 · arxiv created 2011/12/16 · arxiv updated 2011/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We first show that stationary black holes satisfy an extremely simple local form of the first law δE=κ(l) δA/(8 π) where the thermodynamical energy E=A/(8πl) and (local) surface gravity κ(l)=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.

Cited by

• Horizon energy as the boost boundary term in general relativity and loop gravity
• Quantum Hall Effect and Black Hole Entropy in Loop Quantum Gravity

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