Related papers: Recent results in mathematical relativity
We derive a local curvature estimate for four-dimensional stationary solutions to the inheriting Einstein-Maxwell-Klein-Gordon equations. In particular, it implies that any such stationary geodesically complete solution with vanishing…
We construct low regularity solutions of the vacuum Einstein constraint equations. In particular, on 3-manifolds we obtain solutions with metrics in $H^s\loc$ with $s>{3\over 2}$. The theory of maximal asymptotically Euclidean solutions of…
Table of contents: Editorial 1 Correspondents 3 Some recent work in general relativistic Astrophysics 4 Two dimensional black holes 6 Resonant-mass gravitational wave detectors: an update 8 Universality and scaling in gravitational collapse…
Numerical Relativity is concerned with solving the Einstein equations, as well as any field or matter equations on curved space-time, by means of computer calculations. The methods developed for this purpose up to now, as well as the…
This paper is the fourth in a series dedicated to the mathematically rigorous asymptotic analysis of gravitational radiation under astrophysically realistic setups. It provides an overview of the physical ideas involved in setting up the…
We present a four-dimensional Planck-scale corrected quadratic extension of General Relativity (GR) where no a priori relation between metric and connection is imposed (Palatini formalism). Static spherically symmetric electrovacuum…
We discuss static spherically symmetric solutions in a recently proposed non-local infrared modification of Einstein equations induced by a term $m^2g_{\mu\nu}\Box^{-1} R$, where $m$ is a mass scale. We find that, contrary to what happens…
Cylindrical-like coordinates for constant-curvature 3-spaces are introduced and discussed. This helps to clarify the geometrical properties, the coordinate ranges and the meaning of free parameters in the static vacuum solution of Linet and…
A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious…
We review some modified gravity models which describe the gravitational dark energy and the possibility of cosmic speed-up. The new consistent version of such theory which contains inverse and HD curvature terms as well as new type of…
The problem of deforming geometries is particularly important in the context of constructing new exact solutions of Einstein's equation. This issue often appears when extensions of the general relativity are treated, for instance in brane…
We continue our investigation of the configuration space of general relativity begun in I (gr-qc/9411009). Here we examine the Hamiltonian constraint when the spatial geometry is momentarily static (MS). We show that MS configurations…
We submit the viewpoint that, perhaps, some of the controversies in gravitation occurred during this century are not due to insufficiencies of Einstein's field equations, but rather to insufficiencies in the mathematics used for their…
In this paper we study the spacelike-characteristic Cauchy problem for the Einstein vacuum equations. We prove that given initial data on a maximal compact spacelike hypersurface $\Sigma \simeq \overline{B(0,1)} \subset \mathbb{R}^3$ and…
We show the stability of the geometric optics approximation in general relativity by constructing a family $(g_\lambda)_{\lambda\in(0,1]}$ of high-frequency metrics solutions to the Einstein vacuum equations in 3+1 dimensions without any…
We discuss the linearization of Einstein equations in the presence of a cosmological constant, by expanding the solution for the metric around a flat Minkowski space-time. We demonstrate that one can find consistent solutions to the…
A brief account of the present status of the recent nonlocal generalization of Einstein's theory of gravitation is presented. The main physical assumptions that underlie this theory are described. We clarify the physical meaning and…
This thesis describes the application of numerical techniques to solve Einstein's field equations in three distinct cases. First we present the first long-term stable second order convergent Cauchy characteristic matching code in…
A new approximate solution of vacuum and stationary Einstein field equations is obtained. This solution is constructed by means of a power series expansion of the Ernst potential in terms of two independent and dimensionless parameters…
We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…