2016/05/15 by Stefano Borghini, Lorenzo Mazzieri
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Boundary (topology) #Computer science #Constant (computer programming) #Cosmological constant #Cosmology and Gravitation Theories #De Sitter space #De Sitter universe #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Monotonic function #Physics #Quantum mechanics #Symmetry (geometry) #Theoretical physics #Uniqueness #Universe #Zero (linguistics) #math.AP #math.DG #msc:35B06 #msc:35N25 #msc:53C21
paper · pdf · doi:10.1007/978-3-030-18921-1_3
published as In: Dipierro S. (eds) Contemporary Research in Elliptic PDEs and Related Topics. Springer, Cham (2019) 129-202 · 43 pages. arXiv admin note: substantial text overlap with arXiv:1504.04563
arxiv created 2016/05/15 · openalex publication_date 2019/01/01 · arxiv updated 2022/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we study non-singular vacuum static space-times with non-zero cosmological constant. We introduce new integral quantities, and under suitable assumptions we prove their monotonicity along the level set flow of the static potential. We then show how to use these properties to derive a number of sharp geometric and analytic inequalities, whose equality case can be used to characterize the rotational symmetry of the underlying static solutions. As a consequence, we are able to prove some new uniqueness statements for the de Sitter and the anti-de Sitter metrics. In particular, we show that the de Sitter solution has the least possible surface gravity among three-dimensional static metrics with connected boundary and positive cosmological constant.