Related papers: Solution-generating methods of Einstein's equation…
Relativistic simulations in 3+1 dimensions typically monitor the Hamiltonian and momentum constraints during evolution, with significant violations of these constraints indicating the presence of instabilities. In this paper we rewrite the…
The special conformal transformation (composed by inversion - translation - inversion) is used to generate a time dependent conformally flat spacetime. In order to be an exact solution of Einstein's equations, we need as a source a stress…
A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian…
We show that to every small and decaying solution of the linearized constraint equations about Minkowski spacetime, one can add a quadratically small correction to obtain a solution of the full constraint equations. Near spacelike infinity,…
Using a metric conformal formulation of the Einstein equations, we develop a construction of 4-dimensional anti-de Sitter-like spacetimes coupled to tracefree matter models. Our strategy relies on the formulation of an initial-boundary…
We expand previous work on an inverse approach to Einstein Field Equations where we include fluids with energy flux and consider the vanishing of the anisotropic stress tensor. We consider the approach using warped product spacetimes of…
An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect fluid solutions of Einstein's equations. For physically relevant…
We prove existence and uniqueness of solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a quantum massive scalar field with arbitrary coupling to the scalar curvature. In the semiclassical…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
In this paper, we elucidate the problem of gravitating Skyrmion governed by field equations of the Einstein-Skyrme system with no potential term in the Bondi coordinate. The spherical symmetry has to be assumed and both the metric functions…
A unified general approach is presented for construction of solutions of the characteristic initial value problems for various integrable hyperbolic reductions of Einstein's equations for space-times with two commuting isometries in General…
We investigate a simple variation of the Generalized Harmonic method for evolving the Einstein equations. A flat space wave equation for metric perturbations is separated from the Ricci tensor, with the rest of the Ricci tensor becoming a…
The canonical formalism of the (2+2) formulation of general relativity of 4 spacetime dimensions is studied under no symmetry assumptions, where the spacetime is viewed as a local product of a 2 dimensional base manifold of Lorentzian…
Certain features associated with the symmetry reduction of the vacuum Einstein equations by two commuting, space-like Killing vector fields are studied. In particular, the discussion encompasses the equations for the Gowdy $T^3$ cosmology…
In numerical relativity simulations with non-trivial matter configurations, one must solve the Hamiltonian and momentum constraints of the ADM formulation for the metric variables in the initial data. We introduce a new scheme based on the…
A Hamiltonian algorithm, both theoretical and numerical, to obtain the reduced equations implementing Pontryagine's Maximum Principle for singular linear-quadratic optimal control problems is presented. This algorithm is inspired on the…
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…
In this article we develop some new existence results for the Einstein constraint equations using the Lichnerowicz-York conformal rescaling method. The mean extrinsic curvature is taken to be an arbitrary smooth function without…
Einstein's system of equations in the ADM decomposition involves two subsystems of equations: evolution equations and constraint equations. For numerical relativity, one typically solves the constraint equations only on the initial time…
Topological gravity is the reduction of Einstein's theory to spacetimes with vanishing curvature, but with global degrees of freedom related to the topology of the universe. We present an exact Hamiltonian lattice theory for topological…