Related papers: The characteristic initial value problem for plane…
In the mathematical physics literature, there are heuristic arguments, going back three decades, suggesting that for an open set of initially smooth solutions to the Einstein-vacuum equations in high dimensions, stable, approximately…
In this paper we consider a static and regular fluid generating a locally spherically symmetric and time-independent space-time and calculate the leading quantum corrections to the metric to first order in curvature. Starting from a…
We prove the spacetime Penrose inequality for asymptotically flat $2(n+1)$-dimensional initial data sets for the Einstein equations, which are invariant under a cohomogeneity one action of $\mathrm{SU}(n+1)$. Analogous results are obtained…
We solve the source free electromagnetic wave equation in Friedmann-Robertson-Walker space-times for curvature $K=0$ and $K=-1$. Deriving a solution expression in the form of spherical means we deduce and compare two properties of the…
A method is presented for solving the characteristic initial value problem for the collision and subsequent nonlinear interaction of plane gravitational or gravitational and electromagnetic waves in a Minkowski background. This method…
In this paper, we present strong numerical evidences that the incompressible axisymmetric Euler equations with degenerate viscosity coefficients and smooth initial data of finite energy develop a potential finite-time locally self-similar…
The initial value problem is introduced after a thorough review of the essential geometry. The initial value equations are put into elliptic form using both conformal transformations and a treatment of the extrinsic curvature introduced…
The weakest known criterion for local rotational symmetry (LRS) in spacetimes of Petrov type D is due to Goode and Wainwright (1986). Here it is shown, using methods related to the Cartan-Karlhede procedure, to be equivalent to local…
We formulate an initial boundary value problem (IBVP) for the vacuum Einstein equations by describing the boundary conditions of a spacetime metric in its associated gauge. This gauge is determined, equivariantly with respect to…
A relativistic cosmological perturbation theory for the Friedmann-Lema\^itre-Robertson-Walker universe is presented that explains the masses and formation times of the first structures in our universe. First, it is shown that, without a…
We adapt Luk's analysis of the characteristic initial value problem in General Relativity to the asymptotic characteristic problem for the conformal Einstein field equations to demonstrate the local existence of solutions in a neighbourhood…
We establish existence and uniqueness results for initial-boundary value problems for transport equations in one space dimension with nearly incompressible velocity fields, under the sole assumption that the fields are bounded. In the case…
We show that in the conformally flat case the Penrose inequality is satisfied for the Schwarzschild initial data with a small addition of the axially symmetric traceless exterior curvature. In this class the inequality is saturated only for…
We describe space--time fluctuations by means of small fluctuations of the metric on a given background metric. From a minimally coupled Klein--Gordon equation we obtain within a weak-field approximation up to second order and an averaging…
We describe the construction of a geometric invariant characterising initial data for the Kerr-Newman spacetime. This geometric invariant vanishes if and only if the initial data set corresponds to exact Kerr-Newman initial data, and so…
We will describe here the structure of singularity forming in gravitational collapse of spherically symmetric inhomogeneous dust. Such a collapse is described by the Tolman-Bondi-Lema{\^i}tre metric. The main new result here relates, in a…
Einstein spacetimes (that is vacuum spacetimes possibly with a non-zero cosmological constant {\Lambda}) with constant non-zero Weyl eigenvalus are considered. For type Petrov II & D this assumption allows one to prove that the non-repeated…
There are a number of reasons to entertain the possibility that locality is violated on microscopic scales, for example through the presence of an infinite series of higher derivatives in the fundamental equations of motion. This type of…
Bondi's approach to the construction of a coordinate system is used with a different choice of gauge, in accordance with which the radial coordinate r is an affine parameter, to cast the metric tensor into a form suitable for use with the…
In a recent work, Ringstr\"om proposed a geometric notion of initial data on big bang singularities. Moreover, he conjectured that initial data on the singularity could be used to parameterize quiescent solutions to Einstein's equations;…