The many ways of the characteristic Cauchy problem

Abstract

We review various aspects of the characteristic initial value problem for the Einstein equations, presenting new approaches to some of the issues arising.

25 pages, a couple of minor changes, version corresponds to the one published in CQG

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• A Fundamental Theorem for Hypersurfaces in Semi-Riemannian Warped Products
• Hypersurface data: General properties and Birkhoff theorem in spherical symmetry
• Quasi-Local Black Hole Horizons: Recent Advances
• Stationary Black Holes as Holographs II
• Wave equations with initial data on compact Cauchy horizons
• Outer Entropy and Quasilocal Energy
• Covariant definition of Double Null Data and geometric uniqueness of the characteristic initial value problem
• Double Null Data and the Characteristic Problem in General Relativity
• On the canonical energy of weak gravitational fields with a cosmological constant $\Lambda \in \mathbb{R}$
• The Taylor expansion at past time-like infinity
• KIDs like cones
• The Bondi-Sachs metric at the vertex of a null cone: axially symmetric vacuum solutions
• Revisiting the characteristic initial value problem for the vacuum Einstein field equations
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• Characteristic initial data and smoothness of Scri. II. Asymptotic expansions and construction of conformally smooth data sets
• Twistor representation of Jackiw-Teitelboim gravity
• Global nonlinear stability of Minkowski space for spacelike-characteristic initial data
• Transverse expansion of the metric at null hypersurfaces I. Uniqueness and application to Killing horizons
• The Hawking Energy on the Past Lightcone in Cosmology
• Cauchy problem with data on a characteristic cone for the Einstein-Vlasov equations
• On the horizon entropy of a causal set
• Outer entropy = Bartnik-Bray inner mass, and the gravitational ant conjecture
• Transverse expansion of the metric at null hypersurfaces II. Existence results and application to Killing horizons
• Multiple Killing Horizons: the initial value formulation for $\Lambda$-vacuum
• Gluing variations
• On the global "two-sided" characteristic Cauchy problem for linear wave equations on manifolds
• Holographic Screen Sequestration
• Cauchy problem on two characteristic hypersurfaces for the Einstein-Vlasov-Scalar field equations in temporal gauge
• On the Initial Data Constraints on the Light cone for the Einstein-Vlasov system