2010/05/31 by Federico Piazza
Mathematics · Physics and Astronomy · #Acceleration #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Closed timelike curve #Computer science #Cosmology and Gravitation Theories #Curvature #Energy condition #Geodesic #Geodesics in general relativity #Geometry #Light cone #Mathematical analysis #Mathematical physics #Mathematics #Null (SQL) #Physics #Quantum mechanics #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.82.084004
published as Phys.Rev.D82:084004,2010 · 8+1 pages, final version
openalex publication_date 2010/10/06 · arxiv created 2010/10/25 · arxiv updated 2014/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is a known result by Jacobson that the flux of energy matter through a local Rindler horizon is related with the expansion of the null generators in a way that mirrors the first law of thermodynamics. We extend such a result to a timelike screen of observers with finite acceleration. Since timelike curves have more freedom than null geodesics, the construction is more involved than Jacobson's and few geometrical constraints need to be imposed: the observers' acceleration has to be constant in time and everywhere orthogonal to the screen. Moreover, at any given time, the extrinsic curvature of the screen has to be flat. The latter requirement can be weakened by asking that the extrinsic curvature, if present at the beginning, evolves in time like on a cone and just rescales proportionally to the expansion.