Related papers: Solution-generating methods of Einstein's equation…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
For a conformally-coupled scalar field we obtain the conformally-related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally-related spacetimes. In particular, we…
In this article, it is shown how the extended conformal Einstein field equations and a gauge based on the properties of conformal geodesics can be used to analyse the non-linear stability of de Sitter-like spacetimes with spatial sections…
We establish the existence of a class of asymptotically Euclidean solutions to Einstein's constraint equations, whose asymptotic behavior at infinity is arbitrarily prescribed. The proposed seed-to-solution method relies on iterations based…
A linear relationship between the Hubble expansion parameter and the time derivative of the scalar field is assumed in order to derive exact analytic cosmological solutions to Einstein's gravity with two fluids: a barotropic perfect fluid…
In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy ${\hat E}_{ADM}$, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of {\it…
We construct high-frequency initial data for the Einstein vacuum equations in dimension 3+1 by solving the constraint equations on $\mathbb{R}^3$. Our family of solutions $(\bar{g}_\lambda,K_\lambda)_{\lambda\in(0,1]}$ is defined through a…
It is shown that the well-known triviality of the Einstein field equations in two dimensions is not a sufficient condition for the Einstein-Hilbert action to be a total divergence, if the general covariance is to be preserved, that is, a…
We show that well-posed, conformally-decomposed formulations of the 3+1 Einstein equations can be obtained by densitizing the lapse and by combining the constraints with the evolution equations. We compute the characteristics structure and…
Gravitational wave solutions to Einstein's equations and their generation are examined in D-dimensional flat spacetimes. First the plane wave solutions are analyzed; then the wave generation is studied with the solution for the metric…
We present the Ernst potential and the line element of an exact solution of Einstein's vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass…
Following a solution generating technique introduced recently by one of us, we transform the Einstein static Universe into a two - fold infinity class of physically acceptable exact perfect fluid solutions of Einstein's equations. Whereas…
We construct new vacuum solutions of the Einstein equations generated from electrovacuum configurations embedded in external electromagnetic backgrounds. Starting from accelerating Bertotti--Robinson black holes, we exploit two independent…
We consider 4-dimensional spacetime manifolds that are piecewise Lorentzian, where the Lorentzian components of the manifold are separated by codimension-one planes (spacelike or timelike) on which the metric is degenerate. Such manifolds…
We study the semiclassical Einstein field equations with a Klein-Gordon field in ultrastatic and static spacetimes. In both cases, the equations for the spacetime metric become constraint equations. In the ultrastatic case, the Hadamard…
In this paper we consider the single patch pseudo-spectral scheme for tensorial and spinorial evolution problems on the 2-sphere presented in [3,4] which is based on the spin-weighted spherical harmonics transform. We apply and extend this…
By their very nature, field-theoretical Hamiltonians are derived in momentum representation. To solve the corresponding integro-differential equations is more difficult than to solve the simpler differential equations in configuration space…
A general covariant extension of Einstein's field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector. The extended field equations,…
Strongly coupled gravitational systems describe Einstein gravity and matter in the limit that Newton's constant G is assumed to be very large. The nonlinear evolution of these systems may be solved analytically in the classical and…
We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor…