The general relativistic constraint equations
Alessandro Carlotto
Abstract
Abstract We present the state-of-the-art concerning the relativistic constraints, which describe the geometry of hypersurfaces in a spacetime subject to the Einstein field equations. We review a variety of solvability results, the construction of several classes of solutions of special relevance and place results in the broader context of mathematical general relativity. Apart from providing an overview of the subject, this paper includes a selection of open questions, as well as a few complements to some significant contributions in the literature.
Topics & Concepts
PhysicsVariety (cybernetics)SpacetimeConstraint (computer-aided design)EinsteinGeneral relativityContext (archaeology)Relevance (law)Theoretical physicsSubject (documents)Theory of relativitySpecial relativityField (mathematics)Field equationClassical mechanicsMathematicsComputer scienceGeometryPure mathematicsQuantum mechanicsPolitical scienceLibrary scienceBiologyStatisticsPaleontologyLawBlack Holes and Theoretical PhysicsCosmology and Gravitation TheoriesGeometric Analysis and Curvature Flows