arXiv research

We present a gluing construction which adds, via a localized deformation, exactly Delaunay ends to generic metrics with constant positive scalar curvature. This provides time-symmetric initial data sets for the vacuum Einstein equations with positive cosmological constant with exactly Kottler-Schwarzschild-de Sitter en…

Proves uniqueness of certain spacetime solutions with extremal horizons.

Constructs many black hole spacetimes in de Sitter space.

In this global study of solutions to the linear wave equation on Schwarzschild de Sitter spacetimes we attend to the cosmological region of spacetime which is bounded in the past by cosmological horizons and to the future by a spacelike hypersurface at infinity. We prove an energy estimate capturing the expansion of th…

We establish a new uniqueness theorem for the three dimensional Schwarzschild-de Sitter metrics. For this some new or improved tools are developed. These include a reverse Lojasiewicz inequality, which holds in a neighborhood of the extremal points of any smooth function. We further prove smoothness of the set of maxim…

We construct large families of initial data sets for the vacuum Einstein equations with positive cosmological constant which contain exactly Delaunay ends; these are non-trivial initial data sets which coincide with those for the Kottler-Schwarzschild-de Sitter metrics in regions of infinite extent. From the purely Rie…

In this work, we consider solutions of the Maxwell equations on the Schwarzschild-de Sitter family of black hole spacetimes. We prove that, in the static region bounded by black hole and cosmological horizons, solutions of the Maxwell equations decay to stationary Coulomb solutions at a super-polynomial rate, with deca…

We give an exhaustive description of bifurcations and of the number of solutions of the vacuum Lichnerowicz equation with positive cosmological constant on $S^1\times S^2$ with $U(1)\times SO(3)$-invariant seed data. The resulting CMC slicings of Schwarzschild-de Sitter and Nariai are described.

We consider solutions to the linear wave equation $\Box_gφ=0$ on a non-extremal maximally extended Schwarzschild-de Sitter spacetime arising from arbitrary smooth initial data prescribed on an arbitrary Cauchy hypersurface. (In particular, no symmetry is assumed on initial data, and the support of the solutions may con…

This paper addresses pure gauge questions in the study of (asymptotically) de Sitter spacetimes. We construct global solutions to the eikonal equation on de Sitter, whose level sets give rise to double null foliations, and give detailed estimates for the structure coefficients in this gauge. We show two results which a…

Study on special anisotropic conformal changes of conic pseudo-Finsler surfaces.

This is the second of two works, in which we discuss the definition of an appropriate notion of mass for static metrics, in the case where the cosmological constant is positive and the model solutions are compact. In the first part, we have established a positive mass statement, characterising the de Sitter solution as…

We develop a gluing construction which adds scaled and truncated asymptotically Euclidean solutions of the Einstein constraint equations to compact solutions with potentially non-trivial cosmological constants. The result is a one-parameter family of initial data which has ordinary and scaled "point-particle" limits an…

Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to construct a noncommutative version of general relativity, which is expected to capt…

We establish a black hole uniqueness theorem for Schwarzschild-de Sitter spacetime, also called Kottler spacetime, which satisfies Einstein's field equations of general relativity with positive cosmological constant. Our result concerns the class of static vacuum spacetimes with compact spacelike slices and regular max…

This paper addresses strong cosmic censorship for spacetimes with self-gravitating collisionless matter, evolving from surface-symmetric compact initial data. The global dynamics exhibit qualitatively different features according to the sign of the curvature $k$ of the symmetric surfaces and the cosmological constant $…

Classification of specific pseudo-Riemannian manifolds.

De Sitter spacetime can be separated into two parts along two kinds of hypersurfaces and the half-de Sitter spacetimes are covered by the planar and hyperbolic coordinates respectively. Two positive energy theorems were proved previously for certain $¶$-asymptotically de Sitter and $\H$-asymptotically de Sitter initial…

Proves optimal isoperimetric inequality in de Sitter space.

Study examines solutions to Jang equation on anti-de Sitter spacetimes.

Proof of Tholozan's volume formula for anti-de-Sitter 3-manifolds.

Estimates for spacelike hypersurfaces in de Sitter space.

Link between Teichmüller and anti de Sitter geometry via length functions.

Combines non-Euclidean and de Sitter geometries on the plane.

The paper classifies surfaces with constant curvature in 3D De Sitter and anti De Sitter spaces.

Study subelliptic heat kernel on octonionic anti-de Sitter space.

Study flow on de Sitter space for convex hypersurfaces.

The paper characterizes timelike rectifying curves in De Sitter 3-space.

Formulas derived for operators on forms in anti-de Sitter spaces.

Study domination between non-Fuchsian surface group representations and anti-de Sitter geometry.

Paper extends positive energy theorem to anti-de Sitter spacetimes.

Paper proves rigidity for certain spacelike hypersurfaces in de Sitter space.

Study on compact biconservative hypersurfaces in de Sitter space.

Paper finds minimum volume for specific anti-de Sitter 3-manifolds.

Study classifies metrics on anti-de Sitter spacetime with specific symmetries.

Anti-de Sitter spacetimes with convex boundaries are uniquely determined by their boundary metrics.

The paper proves uniqueness of closed timelike geodesics on de-Sitter tori with one singularity.

Solves Dirichlet problem for prescribed scalar curvature in Anti-de Sitter space

Study of 2D Lorentzian anti-de Sitter plane using geometric control theory.

We study geodesics along a noncompact Kerr-Newman instanton, where the asymptotic geometry is either de Sitter or anti-de Sitter. We use first integrals for the Hamilton-Jacobi equation to characterize trajectories both near and away from horizons. We study the interaction of geodesics with special features of the metr…

We establish the inequality for Henneaux-Teitelboim's total energy-momentum for asymptotically anti-de Sitter initial data sets which are asymptotic to arbitrary $t$-slice in anti-de Sitter spacetime. In particular, when $t=0$, it generalizes Chruściel-Maerten-Tod's inequality in the center of AdS mass coordinates. We …

The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY) tensor as a ``hidden'' symmetry which provides the separation of variables for the geodesic…

The paper proves geometric inequalities for pinched convex hypersurfaces in de Sitter space.

In this paper, we generalize the defining equation for de Sitter space by replacing the de Sitter radius with a function $f$ satisfying certain conditions; each resulting hypersurface is diffeomorphic to de Sitter space, and has a geometry (and causal character) which is controlled by the choice of $f$. Necessary and s…

Study null surfaces of pseudo-spherical curves in anti-de Sitter space.

Adds charged black holes to de Sitter space.

Study characterizes conformal boundaries of de Sitter spacetimes.

Study finds necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.