Related papers: Recent results in mathematical relativity
This thesis is concerned with global properties of those cosmological solutions of Einstein's field equations which obey accelerated expansion into the future driven by a non-vanishing cosmological constant, as suggested by current…
We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…
Assuming the four-dimensional space-time to be a general warped product of two surfaces we reduce the four-dimensional Einstein equations to a two-dimensional problem which can be solved. All global vacuum solutions are explicitly…
It is well-known that the Einstein-Rosen solutions to the 3+1 dimensional vacuum Einstein's equations are in one to one correspondence with solutions of 2+1 dimensional general relativity coupled to axi-symmetric, zero rest mass scalar…
We review recent mathematical results concerning the high-frequency solutions to the Einstein vacuum equations and the limits of these solutions. In particular, we focus on two conjectures of Burnett, which attempt to give an exact…
The intimate relations between Einstein's equation, conformal geometry, geometric asymptotics, and the idea of an isolated system in general relativity have been pointed out by Penrose many years ago. A detailed analysis of the interplay of…
After a brief chronological sketch of developments in non-perturbative canonical quantum gravity, some of the recent mathematical results are reviewed. These include: i) an explicit construction of the quantum counterpart of Wheeler's…
The recent observational data in cosmology seem to indicate that the universe is currently expanding in an accelerated way. An intriguing interpretation of these data is that they may just be signalling that Einstein's General Relativity is…
An immense class of physical counterexamples to the four dimensional strong cosmic censor conjecture---in its usual broad formulation---is exhibited. More precisely, out of any closed and simply connected 4-manifold an open Ricci-flat…
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…
Critical gravitational collapse offers a unique window into regimes of arbitrarily high curvature, culminating in a naked singularity arising from smooth initial data -- thus providing a dynamical counterexample to weak cosmic censorship.…
We show that any solution of the 4D Einstein equations of general relativity in vacuum with a cosmological constant may be embedded in a solution of the 5D Ricci-flat equations with an effective 4D cosmological "constant" that is a specific…
We review recent results by the author, in collaboration with Erwann Delay, Olivier Lengard, and Rafe Mazzeo, on existence and properties of space-times with controlled asymptotic behavior at null infinity.
We give a short proof of the existence of a small piece of null infinity for $(3+1)$-dimensional spacetimes evolving from asymptotically flat initial data as solutions of the Einstein vacuum equations. We introduce a modification of the…
We review recent progress in taking the large dimension limit of Einstein's equations. Most of our analysis is classical in nature and concerns situations where there is a black hole horizon although we briefly discuss various extensions…
We obtain a general five dimensional (5D) quasispherical solutions of irrotational dust in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms. These solutions are generalization, to Einstein-Gauss-Bonnet…
We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possess the following remarkable…
The global existence of smooth solutions to the vacuum free boundary problem with physical singularity of compressible Euler equations with damping and gravity is proved in space dimensions $n=1, 2, 3$, for the initial data being small…
The physical consistency of the match of piecewise-$C^0$ metrics is discussed. The mathematical theory of gravitational discontinuity hypersurfaces is generalized to cover the match of regularly discontinuous metrics. The mean-value…
The cosmological constant and its phenomenology remain among the greatest puzzles in theoretical physics. We review how modifications of Einstein's general relativity could alleviate the different problems associated with it that result…