On the Uniqueness of Schwarzschild–de Sitter Spacetime
Stefano Borghini, Piotr T. Chruściel, Lorenzo Mazzieri
Abstract
We establish a new uniqueness theorem for the three dimensional Schwarzschild-de Sitter metrics. For this, some new or improved tools are developed. These include a reverse Łojasiewicz inequality, which holds in a neighborhood of the extremal points of any smooth function. We further prove the smoothness of the set of maxima of the lapse, whenever this set contains a topological hypersurface. This leads to a new strategy for the classification of well behaved static solutions of vacuum Einstein equations with a positive cosmological constant, based on the geometry of the maximum-set of the lapse.
Topics & Concepts
HypersurfaceUniquenessSchwarzschild radiusDe Sitter universeCosmological constantSmoothnessSpacetimeConstant (computer programming)Mathematical physicsMathematicsFunction (biology)UniverseEinsteinPhysicsMathematical analysisPure mathematicsQuantum mechanicsComputer scienceProgramming languageBiologyEvolutionary biologyAdvanced Differential Geometry ResearchBlack Holes and Theoretical PhysicsCosmology and Gravitation Theories