Related papers: Solving the Einstein Equations Numerically
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is…
We consider the 3-dimensional formulation of Einstein's theory for spacetimes possessing a non-null Killing field $\xi^a$. It is known that for the vacuum case some of the basic field equations are deducible from the others. It will be…
This talk reports on the status of an approach to the numerical study of isolated systems with the conformal field equations. We first describe the algorithms used in a code which has been developed at AEI in the last years, and discuss a…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…
We try to lay down the foundations of a Newtonian theory where inertia and gravitational fields appear in a unified way aiming to reach a better understanding of the general relativistic theory. We also formulate a kind of equivalence…
An introduction into the fundamental quests addressed in space missions is given. These quests are the exploration of the relativistic gravitational field, the Universality of Free Fall, the Universality of the Gravitational Redshift, Local…
We are concerned with the numerical solution of a class integro-differential equations, known as Neural Field Equations, which describe the large-scale dynamics of spatially structured networks of neurons. These equations have many…
We discuss a successful three-dimensional cartesian implementation of the Bona-Mass\'o hyperbolic formulation of the 3+1 Einstein evolution equations in numerical relativity. The numerical code, which we call ``Cactus,'' provides a general…
The nature of gravity is fundamental to understand the scaffolding of the Universe and its evolution. Einstein's general theory of relativity has been scrutinized for over ninety five years and shown to describe accurately all phenomena…
Our conventional understanding of space-time, as well as our notion of geometry, break down once we attempt to describe the very early stages of the evolution of our universe. The extreme physical conditions near the Big Bang necessitate an…
Einstein's theory of general relativity describes gravity as the interaction of particles with space-time geometry, as opposed to interacting with a physical fluid, as in the old gravitational aether theories. Moreover, any theoretical…
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,…
In this paper, we present a series of techniques to describe General Relativity using Geometric Algebra (GA). We emphasize the physical interpretation of quantities and provide a step-by-step guide for performing calculations. In doing so,…
The mathematical concept of the Newtonian limit of Einstein's field equations in the expanding Friedmann universe is formulated. The geodesic equations of motion of planets and light are derived and compared.
Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic…
Spherically symmetric (1D) black-hole spacetimes are considered as a test for numerical relativity. A finite difference code, based in the hyperbolic structure of Einstein's equations with the harmonic slicing condition is presented.…
Numerical relativity has made big strides over the last decade. A number of problems that have plagued the field for years have now been mostly solved. This progress has transformed numerical relativity into a powerful tool to explore…
General relativity describes the gravitational field geometrically and in a self-interacting way because it couples to all forms of energy, including its own. Both features make finding a quantum theory difficult, yet it is important in the…
We perform large-scale cosmological simulations that solve Einstein's equations directly via numerical relativity. Starting with initial conditions sampled from the cosmic microwave background, we track the emergence of a cosmic web without…