Erwann Delay

Existence of non-trivial, vacuum, asymptotically simple spacetimes

We construct non-trivial vacuum space-times with a global Scri. The construction proceeds by proving extension results across compact boundaries for initial data sets, adapting the gluing arguments of Corvino and Schoen. Another application of the extension results is existence of initial data which are exactly Schwarzschild both near infinity and near each of the connected component of the apparent horizon.A method is described of programming a memory array on a single integrated circuit so that a portion of each data word is characterized as CAM, with the remaining portion of each data word functioning as RAM. The programmable memory array is partitioned into CAM and RAM subfields by disabling the comparators in each memory cell in selected columns of CAM cells to create RAM-functioning cells. Said partitioning may be re-programmed to enable the comparators in said RAM-functioning cells to be re-enabled, so that said cells may participate in subsequent comparisons to a search word. The described memory array permits direct retrieval and storage of associated information in RAM-functioning cells corresponding to data words which are determined to match a given search word. This direct retrieval and storage process can efficiently be utilized without computing or decoding an address for the associated information.

Non-trivial, static, geodesically complete, vacuum space-times with a negative cosmological constant

We construct a large class of new singularity-free static lorentzian four-dimensional solutions of the vacuum Einstein equations with a negative cosmological constant. The new families of metrics contain space-times with, or without, black hole regions. Two uniqueness results are also established.

Non-Singular, Vacuum, Stationary Space-Times with a Negative Cosmological Constant

We construct infinite dimensional families of non-singular stationary space times, solutions of the vacuum Einstein equations with a negative cosmological constant.

Essential spectrum of the Lichnerowicz Laplacian on two tensors on asymptotically hyperbolic manifolds

Abstract On an n -dimensional asymptotically hyperbolic manifold with n >2, we show that the essential spectrum of the Lichnerowicz Laplacian acting on trace free symmetric covariant two tensors is the ray [( n −1)( n −9)/4,+∞[. For the particular case of the hyperbolic space, this is the spectrum.

Étude locale d'opérateurs de courbure sur l'espace hyperbolique

Abstract We show in this article that, on the unit ball in, the operators of covariant and contravariant Ricci curvature, and of Einstein curvature, are locally invertible in a neighborhood of the hyperbolic metric h 0 . We deduce in the C ∞ case that the image of the Riemann-Christoffel curvature operator is a submanifold in a neighborhood of h 0 . We deal also with some obstructions related to the asymptotic behavior of metrics near h 0 , and we treat more precisely the case of the Ricci equation in dimension 2.

Non-trivial, static, geodesically complete space-times with a negative cosmological constant II. n ≥ 5

We show that the recent work of Lee [23] implies existence of a large class of new singularity-free strictly static Lorentzian vacuum solutions of the Einstein equations with a negative cosmological constant. This holds in all space-time dimensions greater than or equal to four, and leads both to strictly static solutions and to black hole solutions. The construction allows in principle for metrics (whether black hole or not) with Yang-Mills-dilaton fields interacting with gravity through a Kaluza-Klein coupling.

Non-singular space-times with a negative cosmological constant: II. Static solutions of the Einstein–Maxwell equations

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.

Ricci curvature in the neighborhood of rank-one symmetric spaces

We study the Ricci curvature of a Riemannian metric as a differential operator acting on the space of metrics close (in a weighted functional spaces topology) to the standard metric of a rank-one noncompact symmetric space. We prove that any symmetric bilinear field close enough to the standard may be realized as the Ricci curvature of a unique close metric if its decay rate at infinity (its weight) belongs to some precisely known interval. We also study what happens if the decay rate is too small or too large.

Nonsingular spacetimes with a negative cosmological constant: Stationary solutions with matter fields

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.

Non-singular spacetimes with a negative cosmological constant: IV. Stationary black hole solutions with matter fields

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-