2015/10/13 by Piermarco Fonda, Domenico Seminara, Erik Tonni · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Curvature #Entropy (arrow of time) #Geodesic #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum entanglement #Quantum mechanics #Scalar curvature #Sectional curvature #Spacetime #Submanifold #Willmore energy #cond-mat.str-el #gr-qc #hep-th
paper · pdf · doi:10.1007/jhep12(2015)037
published as JHEP 1512 (2015) 037 · 49 pages, 11 figures
arxiv created 2015/10/13 · openalex publication_date 2015/12/01 · arxiv updated 2015/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the finite term of the holographic entanglement entropy of finite domains with smooth shapes and for four dimensional gravitational backgrounds. Analytic expressions depending on the unit vectors normal to the minimal area surface are obtained for both stationary and time dependent spacetimes. The special cases of AdS4, asymptotically AdS4 black holes, domain wall geometries and Vaidya-AdS backgrounds have been analysed explicitly. When the bulk spacetime is AdS4, the finite term is the Willmore energy of the minimal area surface viewed as a submanifold of the three dimensional flat Euclidean space. For the static spacetimes, some numerical checks involving spatial regions delimited by ellipses and non convex domains have been performed. In the case of AdS4, the infinite wedge has been also considered, recovering the known analytic formula for the coefficient of the logarithmic divergence.