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We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the…
This article solves the initial boundary value problem for the vacuum Einstein equations with a negative cosmological constant in dimension 4, giving rise to asymptotically Anti-de Sitter spaces. We introduce a new family of geometric…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
The theory of macroscopic gravity provides a formalism to average the Einstein field equations from small scales to largest scales in space-time. It is well known that averaging is an operation that does not commute with calculating the…
In this article, we present a gravitational collapse null dust solution of the Einstein field equations. The spacetime is regular everywhere except on the symmetry axis where it possesses a naked curvature singularity, and admits one…
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…
Green and Wald have presented a mathematically rigorous framework to study, within general relativity, the effect of small scale inhomogeneities on the global structure of space-time. The framework relies on the existence of a one-parameter…
In this article we study self-gravitating static solutions of the Einstein-ScalarField system in arbitrary dimensions. We discuss the existence and the non-existence of geodesically complete solutions depending on the form of the scalar…
The present work concerns the derivation of a numerical scheme to approximate weak solutions of the Euler equations with a gravitational source term. The designed scheme is proved to be fully well-balanced since it is able to exactly…
A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially…
We find solutions of Einstein's field equation for topologically stable strings associated with the breaking of a U(1) symmetry. Strings form in many GUTs and are expected whenever the homotopy group $\Pi_1(M_0)$ is non-trivial. The…
By employing the Bianchi identities for the Riemann tensor in conjunction with the Einstein equations, we construct a first order symmetric hyperbolic system for the evolution part of the Cauchy problem of general relativity. In this…
Einstein gravity coupled to a massive skew symmetric field F_{\mu\nu\lambda} leads to an acceleration law that modifies the Newtonian law of attraction between particles. We use a framework of non-perturbative renormalization group…
Exact solutions of Einstein's vacuum equations are considered which describe gravitational waves with distinct wavefronts. A family of such solutions presented recently in which the wavefronts have various geometries and which propagate…
Considering a five-dimensional (5D) Riemannian spacetime with a particular stationary Ricci-flat metric, we obtain in the framework of the induced matter theory an effective 4D static and spherically symmetric metric which give us ordinary…
We present a physically plausible solution representing Einstein's cluster mimicking the behaviors of compact star in the context of teleparallel equivalent of general relativity. The Teleparallel gravity (TEGR) is an alternative…
We prove global existence for Einstein's equations with a charged scalar field for initial conditions sufficiently close to the Minkowski spacetime without matter. The proof relies on generalized wave coordinates adapted to the outgoing…
Hybrid inverse problems are based on the interplay of two types of waves, in order to allow for imaging with both high resolution and high contrast. The inversion procedure often consists of two steps: first, internal measurements involving…
Using the renormalization group method, we improved the first order solution of the long-wavelength expansion of the Einstein equation. By assuming that the renormalization group transformation has the property of Lie group, we can…
As it is well known, the global structure of the Einstein equations for general relativity in the context of the initial value problem, is a difficult and intricate mathematical problem. Therefore, any additional structure in their…