Related papers: Dressing with Control: using integrability to gene…
In this work we study the 2+1 Einstein-Klein-Gordon system in the framework of Gravitational Decoupling. We associate the generic matter decoupling sector with a real scalar field so we can obtain a constraint which allows to close the…
Integrable structures arise in general relativity when the spacetime possesses a pair of commuting Killing vectors admitting 2-spaces orthogonal to the group orbits. The physical interpretation of such spacetimes depends on the norm of the…
In this work we propose a new procedure for to extract global information of a space-time. We considered a space-time immersed in a higher dimensional space and we formulate the equations of Einstein through of the Frobenius conditions to…
We establish the linear instability of the semiclassical Einstein-Klein-Gordon system linearised about the Minkowski vacuum spacetime. The proof relies on formulating a forcing problem for both metric and state perturbations within the…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
We illustrate the mass and charge renormalization procedures in quantum field theory using, as an example, a simple model of interacting electrons and photons. It is shown how addition of infinite renormalization counterterms to the…
A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime. Since Einstein's equations follow from varying the action, it should be possible to derive them by…
We find and analyse solutions of Einstein's equations in arbitrary d dimensions and in the presence of a scalar field with a Liouville potential coupled to a Maxwell field. We consider spacetimes of cylindrical symmetry or again subspaces…
We give a general survey of the solution of the Einstein constraints by the conformal method on n dimensional compact manifolds. We prove some new results about solutions with low regularity (solutions in $H_{2}$ when n=3), and solutions…
The Einstein equations have proven surprisingly difficult to solve numerically. A standard diagnostic of the problems which plague the field is the failure of computational schemes to satisfy the constraints, which are known to be…
In this paper, we present a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can…
In symbolic integration, the Risch--Norman algorithm aims to find closed forms of elementary integrals over differential fields by an ansatz for the integral, which usually is based on heuristic degree bounds. Norman presented an approach…
The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's…
This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…
I present a new, simple method to dynamically control the growth of the discretized constraints during a free evolution of Einstein's equations. During an evolution, any given family of formulations is adjusted off the constraints surface…
We employ the gravitational decoupling approach for static and spherically symmetric systems to develop a simple and powerful method in order to a) continuously isotropize any anisotropic solution of the Einstein field equations, and b)…
We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry,…
Multidimensional cosmological models with $n~(n > 1)$ Einstein spaces are discussed classically and with respect to canonical quantization. These models are integrable in the case of Ricci flat internal spaces. For negative curvature of the…
Starting with the most general four-dimensional spacetime possessing two commuting Killing vectors and a nontrivial Killing tensor, we analytically integrate Einstein-Yang-Mills equations for a completely arbitrary gauge group. It is…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…