Julien Cortier

On the center of mass of asymptotically hyperbolic initial data sets

We define the (total) center of mass for suitably asymptotically hyperbolic time-slices of asymptotically anti-de Sitter spacetimes in general relativity. We do so in analogy to the picture that has been consolidated for the (total) center of mass of suitably asymptotically Euclidean time-slices of asymptotically Minkowskian spacetimes (isolated systems). In particular, we unite—an altered version of—the approach based on Hamiltonian charges with an approach based on CMC-foliations near infinity. The newly defined center of mass transforms appropriately under changes of the asymptotic coordinates and evolves in the direction of an appropriately defined linear momentum under the Einstein evolution equations.

Gluing Construction of Initial Data with Kerr–de Sitter Ends

We construct initial data sets which satisfy the vacuum constraint equations of General Relativity with positive cosmological constant. More precisely, we deform initial data with ends asymptotic to Schwarzschild–de Sitter to obtain non-trivial initial data with exactly Kerr–de Sitter ends. The method is inspired from Corvino’s gluing method. We obtain here a extension of a previous result for the time-symmetric case by Chruściel and Pollack (Ann H Poincaré 9(4):639–654, 2008). We also deal with the case of asymptotically Kerr–de Sitter initial data.

A family of asymptotically hyperbolic manifolds with arbitrary energy-momentum vectors

A family of non-radial solutions to the Yamabe equation, modeled on the hyperbolic space, is constructed using power series. As a result, we obtain a family of asymptotically hyperbolic metrics, with spherical conformal infinity, with scalar curvature greater than or equal to −n(n − 1), but which are a priori not complete. Moreover, any vector of Rn+1 is performed by an energy-momentun vector of one suitable metric of this family. They can in particular provide counter-examples to the positive energy-momentum theorem when one removes the completeness assumption.

On the Structure of the Ergosurface of Pomeransky-Senkov Black Rings

We study the properties of the ergosurface of the Pomeransky–Senkov black rings, and show that it splits into an “inner” and an “outer” region. As for the singular set, the topology of the “outer ergosurface” depends upon the value of parameters.