Related papers: Solving the Einstein Equations Numerically
Initial data are the starting point for any numerical simulation. In the case of numerical relativity, Einstein's equations constrain our choices of these initial data. We will examine several of the formalisms used for specifying Cauchy…
A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at…
When four-dimensional general relativity is embedded in an unconstrained man-ner in a fifth dimension, the physical quantities of spacetime can be interpreted as geometrical properties related to the extra dimension. It has become…
It is very likely that the quantum description of spacetime is quite different from what we perceive at large scales, $l\gg (G\hbar/c^3)^{1/2}$. The long wave length description of spacetime, based on Einstein's equations, is similar to the…
In this work a study of the gravity is made using Einstein's equation in the post-Newtonian approach. This is a method to linearise the General Relativity indicated to treat non-relativistic objects. It enables us to construct, from…
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing…
Numerical relativity is finally coming of age with the development of massively parallel computers. 3D problems, which were completely intractable several years ago due to limited computer power, can now be performed with grid sizes of…
Spacetime is foliated by spatial hypersurfaces in the 3+1 split of General Relativity. The initial value problem then consists of specifying initial data for all relevant fields on one such a spatial hypersurface. These fields are the…
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical…
Contents: 1) Introduction and a few excursions [A word on the role of explicit solutions in other parts of physics and astrophysics. Einstein's field equations. "Just so" notes on the simplest solutions: The Minkowski, de Sitter and anti-de…
Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…
Numerical relativity has come a long way in the last three decades and is now reaching a state of maturity. We are gaining a deeper understanding of the fundamental theoretical issues related to the field, from the well posedness of the…
We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for…
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…
This is a brief introduction to general relativity, designed for both students and teachers of the subject. While there are many excellent expositions of general relativity, few adequately explain the geometrical meaning of the basic…
This thesis focuses on the application of numerical relativity methods to the solutions of problems in strong gravity. Our goal is the study of mergers of compact objects in the strong field regime where non-linear dynamics manifest and…
Advances in our understanding of the origin, evolution and structure of the universe have long been driven by cosmological perturbation theory, model building and effective field theory. In this review, we introduce numerical relativity as…
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…
We discuss the issue of radiation extraction in asymptotically flat space-times within the framework of conformal methods for numerical relativity. Our aim is to show that there exists a well defined and accurate extraction procedure which…