114 citations · 456 across the 23 of their papers we have counts for
16 papers · 1 filter
Causal geodesic incompleteness of spacetimes arising from IMP gluing
Madeleine Burkhart, Daniel Pollack
In 2002, Isenberg-Mazzeo-Pollack (IMP) constructed a series of vacuum initial data sets via a gluing construction. In this paper, we investigate some local geometry of these initia…
Null geodesic incompleteness of spacetimes with no CMC Cauchy surfaces
Madeleine Burkhart, Martin Lesourd, Daniel Pollack
Chruściel, Isenberg, and Pollack constructed a class of vacuum cosmological spacetimes that do not admit Cauchy surfaces with constant mean curvature. We prove that, for sufficient…
On the geometry and topology of initial data sets with horizons
Lars Andersson, Mattias Dahl, Gregory J. Galloway +1
We study the relationship between initial data sets with horizons and the existence of metrics of positive scalar curvature. We define a Cauchy Domain of Outer Communications (CDOC…
Topological censorship from the initial data point of view
Michael Eichmair, Gregory J. Galloway, Daniel Pollack
We introduce a natural generalization of marginally outer trapped surfaces, called immersed marginally outer trapped surfaces, and prove that three dimensional asymptotically flat…
Mathematical general relativity: a sampler
Piotr T. Chruściel, Gregory J. Galloway, Daniel Pollack
We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.
Singular Yamabe metrics and initial data with exactly Kottler-Schwarzschild-de Sitter ends II. Generic metrics
Piotr T. Chrusciel, Frank Pacard, Daniel Pollack
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-symme…
Singular Yamabe metrics and initial data with exactly Kottler-Schwarzschild-de Sitter ends
Piotr T. Chrusciel, Daniel Pollack
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 in…
A variational analysis of Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds
Emmanuel Hebey, Frank Pacard, Daniel Pollack
We establish new existence and non-existence results for positive solutions of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This equation arises from the H…
Applications of theorems of Jean Leray to the Einstein-scalar field equations
Yvonne Choquet-Bruhat, James Isenberg, Daniel Pollack
The Einstein-scalar field theory can be used to model gravitational physics with scalar field matter sources. We discuss the initial value formulation of this field theory, and sho…
The constraint equations for the Einstein-scalar field system on compact manifolds
Yvonne Choquet-Bruhat, James Isenberg, Daniel Pollack
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of non…
The Einstein-scalar field constraints on asymptotically Euclidean manifolds
Yvonne Choquet-Bruhat, James Isenberg, Daniel Pollack
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matt…
A gluing construction for non-vacuum solutions of the Einstein constraint equations
James Isenberg, David Maxwell, Daniel Pollack
We extend the conformal gluing construction of Isenberg-Mazzeo-Pollack [18] by establishing an analogous gluing result for field theories obtained by minimally coupling Einstein's…
Gluing Initial Data Sets for General Relativity
Piotr T. Chrusciel, James Isenberg, Daniel Pollack
We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data…
Initial data engineering
Piotr T. Chrusciel, James Isenberg, Daniel Pollack
We present a local gluing construction for general relativistic initial data sets. The method applies to generic initial data, in a sense which is made precise. In particular the t…
On the topology of vacuum spacetimes
James Isenberg, Rafe Mazzeo, Daniel Pollack
We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n+1)-dimensions. We do this by gluing a soluti…
Gluing and wormholes for the Einstein constraint equations
James Isenberg, Rafe Mazzeo, Daniel Pollack
We establish a general gluing theorem for constant mean curvature solutions of the vacuum Einstein constraint equations. This allows one to take connected sums of solutions or to g…