Related papers: Dressing with Control: using integrability to gene…
We apply a dressed perturbation theory to better organize and economize the computation of high orders of the 2-body effective action of an inspiralling Post-Newtonian gravitating binary. We use the effective field theory approach with the…
In this paper, we develop the dressing method to study the exact solutions for the vector sine-Gordon equation. The explicit formulas for one kink and one breather are derived. The method can be used to construct multi-soliton solutions.…
The purpose of this paper is to demonstrate a new method of generating exact solutions to the Einstein's equations obtained by the Hamiltonian reduction. The key element to the successful Hamiltonian reduction is finding the privileged…
The intimate relations between Einstein's equation, conformal geometry, geometric asymptotics, and the idea of an isolated system in general relativity have been pointed out by Penrose many years ago. A detailed analysis of the interplay of…
More than thirty years passed since the first discoveries of various aspects of integrability of the symmetry reduced vacuum Einstein equations and electrovacuum Einstein - Maxwell equations were made and gave rise to constructions of…
Exact solutions to the Einstein field equations may be generated from already existing ones (seed solutions), that admit at least one Killing vector. In this framework, a space of potentials is introduced. By the use of symmetries in this…
The drift method, introduced by the second author, provides a new formulation of the Einstein constraint equations, either in vacuum or with matter fields. The natural of the geometry underlying this method compensates for its slightly…
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 the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form…
Combining incoming and outgoing characteristic formulations can provide numerical relativists with a natural implementation of Einstein's equations that better exploits the causal properties of the spacetime and gives access to both null…
Using holographic-fluid techniques, we discuss some aspects of the integrability properties of Einstein's equations in asymptotically anti-de Sitter spacetimes. We review and we amend the results of 1506.04813 on how exact four-dimensional…
We extend the conformal gluing construction of Isenberg-Mazzeo-Pollack [18] by establishing an analogous gluing result for field theories obtained by minimally coupling Einstein's gravitational theory with matter fields. We treat classical…
This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein field equations using the 1+3 tetrad formalism. This approach reformulates the Einstein equations into first order scalar equations,…
A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the…
This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been…
In principle, global properties of solution of Einstein equations need to be addressed using the conformal Einstein equations, because this conformal compactification allows a clean definition of the `infinities' (spacelike, timelike and…
In this paper we continue the program, initiated in Ref. hep-th/0112246, to investigate an integrable noncommutative version of the sine-Gordon model. We discuss the origin of the extra constraint which the field function has to satisfy in…
We couple a conformal scalar field in (2+1) dimensions to Einstein gravity with torsion. The field equations are obtained by a variational principle. We could not solve the Einstein and Cartan equations analytically. These equations are…
The first step in the building of a spacetime solution of Einstein's gravitational field equations via the initial value formulation is finding a solution of the Einstein constraint equations. We recall the conformal method for constructing…
The effectiveness of the hyperbolic relaxation method for solving the Einstein constraint equations numerically is studied here on a variety of compact orientable three-manifolds. Convergent numerical solutions are found using this method…