Related papers: Recent results in mathematical relativity
This paper gives a detailed pedagogic presentation of the central concepts underlying a new algorithm for the numerical solution of Einstein's equations for gravitation. This approach incorporates the best features of the two leading…
This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein--Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density…
In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric…
We review the properties of the constraint equations, from their geometric origin in hypersurface geometry through to their roles in the Cauchy problem and the Hamiltonian formulation of the Einstein equations. We then review properties of…
We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.
I discuss gauge and global symmetries in particle physics, condensed matter physics, and quantum gravity. In a modern understanding, global symmetries are approximate and gauge symmetries may be emergent. (Based on a lecture at the April,…
We study the properties of compact objects in a particular 4D Horndeski theory originating from higher dimensional Einstein-Gauss-Bonnet gravity. Remarkably, an exact vacuum solution is known. This compact object differs from general…
We prove uniform finite-time existence of solutions to the vacuum Einstein equations in polarized U(1) symmetry which have uniformly positive incoming $H^1$ energy supported on an arbitrarily small set in the 2 + 1 spacetime obtained by…
We discuss the hypothesis of a fixed point for quantum gravity coupled to a scalar, in the limit where the scalar field goes to infinity, accompanied by a suitable scaling of the metric. We propose that no scalar potential is present for…
More than thirty years passed since the first discoveries of various aspects of integrability of the symmetry reduced vacuum Einstein equations and electrovacuum Einstein - Maxwell equations were made and gave rise to constructions of…
This article is dedicated to solving the Einstein constraint equations with apparent horizon boundaries and freely specified mean curvature. The main novelty is that we study the conformal constraint equations assuming only low regularity.
This article gives an elementary overview of the end-state of gravitational collapse according to classical general relativity. The focus of discussion is the formation of black holes and naked singularities in various physically reasonable…
This paper contains results obtained as solutions of the Unified Field Theory equations. It yields space nonlinear oscillations, a quartet of gravitational forces, quintessence, and replaces Einstein's Cosmological Constant by an invariant…
Let $M$ be a connected, simply connected, oriented, closed, smooth four-manifold which is spin (or equivalently having even intersection form) and put $M^\times:=M\setminus\{{\rm point}\}$.In this paper we prove that if $X^\times$ is a…
In this paper we perform systematic investigation of all possible solutions with static compact extra dimensions and expanding three-dimensional subspace (``our Universe''). Unlike previous papers, we consider extra-dimensional subspace to…
We consider self-interacting scalar fields coupled to gravity. Two classes of exact solutions to Einstein's equations are obtained: the first class corresponds to the minimal coupling, the second one to the conformal coupling. One of the…
We review recent progress on the long-time regularity of solutions of the Cauchy problem for the water waves equations, in two and three dimensions. We begin by introducing the free boundary Euler equations and discussing the local…
We consider the most general quadratic in curvature stringy motivated non-local action for the modified Einstein's gravity. We present exact analytic cosmological solutions including the bouncing ones and develop the relevant techniques for…
We perform large-scale cosmological simulations that solve Einstein's equations directly via numerical relativity. Starting with initial conditions sampled from the cosmic microwave background, we track the emergence of a cosmic web without…
The general relativistic non--linear dynamics of a self--gravitating collisionless fluid with vanishing vorticity is studied in synchronous and comoving -- i.e. {\em Lagrangian} -- coordinates. Writing the equations in terms of the metric…