arXiv subjects
Publications and source records attributed to Erwann Delay.
We show that the causal-future-directed character of the energy-momentum vector of $n$-dimensional asymptotically hyperbolic Riemannian manifolds with spherical conformal infinity, $n\ge 3$, can be traced back to that of asymptotically Euclidean general-relativistic initial data sets satisfying the dominant energy condition.
Let (M, g) be a compact Einstein Riemannian manifold with boundary. We show that under certain conditions, the map that associates to a metric on M its Ricci curvature, its induced conformal class on the boundary, and its mean curvature on the boundary is locally invertible near g. The contravariant Ricci operator, as well as other operators such as the Einstein operator, are also studied.
We derive a formula for the energy of asymptotically locally hyperbolic (ALH) manifolds obtained by a gluing at infinity of two ALH manifolds. As an application we show that there exist three-dimensional conformally compact ALH manifolds either without boundary or with toroidal black hole boundary, with connected conformal infinity of higher genus, with constant negative scalar curvature, and with negative mass.
We construct families of asymptotically locally hyperbolic Riemannian metrics with constant scalar curvature (i.e., time symmetric vacuum general relativistic initial data sets with negative cosmological constant), with prescribed topology of apparent horizons and of the conformal boundary at infinity, and with controlled mass. In particular we obtain new classes of solutions with negative mass.
We carry out a Carlotto-Schoen-type gluing with interpolating scalar curvature on cone-like sets, or deformations thereof, in the category of smooth Riemannian asymptotically Euclidean metrics.
We adapt the Bartnik method to provide a Hilbert manifold structure for the space of solutions, without KID's, to the vacuum constraint equations on compact manifold of any dimension $\geq 3$. In the course, we prove that some fibers of the scalar curvature or the constraint operator are Hilbert submanifolds. We also study some operators and inequalities related to the KID's operator. Finally we comment the adaptation to some non compact manifolds.
We prove that the $TT$-gauge-fixed linearised Einstein operator is non-degenerate for Riemannian Kottler ("Schwarzschild-anti de Sitter") metrics with dimension- and topology-dependent ranges of mass parameter. We provide evidence that this remains true for all such metrics except the spherical ones with a critical mass.
We prove existence of large families of solutions of Einstein-complex scalar field equations with a negative cosmological constant, with a stationary or static metric and a time-periodic complex scalar field.
We use an elliptic system of equations with complex coefficients for a set of complex-valued tensor fields as a tool to construct infinite-dimensional families of non-singular stationary black holes, real-valued Lorentzian solutions of the Einstein-Maxwell-dilaton-scalar fields-Yang-Mills-Higgs-Chern-Simons-$f(R)$ equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.
Generalising the results in arXiv:1612.00281, we construct infinite-dimensional families of non-singular stationary space times, solutions of Yang-Mills-Higgs-Einstein-Maxwell-Chern-Simons-dilaton-scalar field equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.
We construct infinite-dimensional families of non-singular static space times, solutions of the vacuum Einstein-Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.
Let (M,g) be a complete noncompact riemannian manifold with bounded geometry and parallel Ricci curvature. We show that some operators, "affine" relatively to the Ricci curvature, are locally invertible, in some classical Sobolev spaces, near the metric g.
Let M be a smooth compact manifold without boundary. We consider two smooth Sub-Semi-Riemannian metrics on M. Under suitable conditions, we show that they are almost conformally isometric in an Lp sense. Assume also that M carries a Riemannian metric with parallel Ricci curvature. Then an equation of Ricci type, is in some sense solvable, without assuming any closeness near a special metric.
We provide a Hilbert manifold structure {à} la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincar{é} and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric.
We propose further conformal parametrizations for initial data in some modified Einstein gravity theories. Some of them give rise to conformally covariant systems.
Let $(M,g)$ be a compact riemannian manifold without boundary., with parallel Rici curvature. We show that some operators, affine relatively to the Ricci curvature,are locally invertible, near the metric $g$
We revisit the Lichnerowicz-York method, and an alternative method of York, in order to obtain some conformally covariant systems. This type of parameterization is certainly more natural for non constant mean curvature initial data.
We show that some curvature operators are locally invertible, in some weithted sobolev spaces, near the euclidian metric. (Nous montrons que certains opérateurs affines en la courbure de Ricci sont localement inversibles, dans des espaces de Sobolev à poids, au voisinage de la métrique euclidienne.)