Bondi-Sachs energy-momentum for the constant mean extrinsic curvature initial value problem

Bondi-Sachs energy-momentum for the constant mean extrinsic curvature initial value problem

The constraints on the asymptotic behavior of the conformal factor and conformal extrinsic curvature imposed by the initial value equations of general relativity on constant mean extrinsic curvature (CMC) hypersurfaces are analyzed in detail. We derive explicit formulas for the Bondi-Sachs energy and momentum in terms of coefficients of asymptotic expansions on CMC hypersurfaces near future nul...

Quasi-localisation of Bondi-Sachs energy loss

Abstract. A formula is given for the variation of the Hawking energy along any oneparameter foliation of compact spatial 2-surfaces. A surface for which one null expansion is positive and the other negative has a preferred orientation, with a spatial or null normal direction being called outgoing or ingoing as the area increases or decreases respectively. A natural way to propagate such a surfa...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Serrin’s Overdetermined Problem and Constant Mean Curvature Surfaces

For all N ≥ 9, we find smooth entire epigraphs in R , namely smooth domains of the form Ω := {x ∈ R / xN > F (x1, . . . , xN−1)}, which are not half-spaces and in which a problem of the form ∆u+ f(u) = 0 in Ω has a positive, bounded solution with 0 Dirichlet boundary data and constant Neumann boundary data on ∂Ω. This answers negatively for large dimensions a question by Berestycki, Caffarelli ...

Bel–robinson Energy and Constant Mean Curvature Foliations

An energy estimate is proved for the Bel–Robinson energy along a constant mean curvature foliation in a spatially compact vacuum spacetime, assuming an L∞ bound on the second fundamental form, and a bound on a spacetime version of Bel–Robinson energy.