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Julien Cortier

Publications and source records attributed to Julien Cortier.

8 recordsLinked to original sources
arXiv2016

Mass-like invariants for asymptotically hyperbolic metrics. Part I: Classification

In this article, we classify the set of asymptotic mass-like invariants for asymptotically hyperbolic metrics. It turns out that the standard mass is just one example among the two families of invariants we find. These invariants correspond to finite-dimensional representations of the group of isometries of hyperbolic space. We describe these invariants in terms of wave-harmonic polynomials and polynomial solutions of the linearized Einstein equations in Minkowski space.

math.DG↗
arXiv2015

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.

math.DG↗
arXiv2014

On complete stationary vacuum initial data

We describe a proof of M.T. Anderson's result on the rigidity of complete stationary initial data for the Einstein vacuum equations in spacetime dimension 3 + 1, under an extra assumption on the norm of the stationary Killing vector field. The argument only involves basic comparison geometry along with some Bochner-Weitzenb\"ock formula techniques. We also discuss on the possibility to extend those techniques in higher dimensions.

gr-qc↗
arXiv2012

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

A family of non-radial solutions of the Yamabe equation, with reference 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 -n(n - 1), but which are a priori not complete. Moreover, any vector of R^n+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.

math.DG↗
arXiv2012

Gluing construction of initial data with Kerr-de Sitter ends

We construct initial data sets which satisfy the vacuum constraint equa- tions of General Relativity with positive cosmologigal constant. More pre- silely, 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.

gr-qc↗
arXiv2010

On the global structure of the Pomeransky-Senkov black holes

We construct analytic extensions of the Pomeransky-Senkov metrics with multiple Killing horizons and asymptotic regions. We show that, in our extensions, the singularities associated to an obstruction to differentiability of the metric lie beyond event horizons. We analyze the topology of the non-empty singular set, which turns out to be parameter-dependent. We present numerical evidence for stable causality of the domain of outer communications. The resulting global structure is somewhat reminiscent of that of Kerr space-time.

gr-qc↗
arXiv2010

Maximal analytic extensions of the Emparan-Reall black ring

We construct a Kruskal-Szekeres-type analytic extension of the Emparan-Reall black ring, and investigate its geometry. We prove that the extension is maximal, globally hyperbolic, and unique within a natural class of extensions. The key to those results is the proof that causal geodesics are either complete, or approach a singular boundary in finite affine time. Alternative maximal analytic extensions are also constructed.

gr-qc↗