Related papers: Regge calculus: a unique tool for numerical relati…
The article presents some aspects on the use of computer in teaching general relativity for undergraduate students with some experience in computer manipulation. The article presents some simple algebraic programming (in REDUCE+EXCALC…
We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly…
These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications:…
The problem of the mutual attraction and joining of two black holes is of importance as both a source of gravitational waves and as a testbed of numerical relativity. If the holes start out close enough that they are initially surrounded by…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
Numerical simulations have become an important tool to understand and predict non-perturbative phenomena in particle physics. In this article we attempt to present a general overview over the field. First, the basic concepts of lattice…
The Regge-Wheeler equation for black-hole gravitational waves is analyzed for large negative imaginary frequencies, leading to a calculation of the cut strength for waves outgoing to infinity. In the--limited--region of overlap, the results…
Relativistic mechanics on an arbitrary manifold is formulated in the terms of jets of its one-dimensional submanifolds. A generic relativistic Lagrangian is constructed. Relativistic mechanics on a pseudo-Riemannian manifold is particularly…
We give a brief summary of results and ongoing research in the application of linearized theory to the study of black hole collisions in the limit in which the holes start close to each other. This approximation can be a valuable tool for…
This review presents an overview of various kinds of models -- physical, abstract, mathematical, visual -- that can be used to present the concepts and applications of Einstein's general theory of relativity at the level of undergraduate…
We introduce a new computer algebra system optimized for use in lattice perturbation theory as well as continuum perturbation theory and a new framework to perform automated perturbative calculations on top of said computer algebra system.…
The uniqueness and rigidity theorems assert that the asymptotically flat, vacuum, stationary rotating black hole solution in general relativity must be the Kerr solution, exhibiting novel symmetries such as axisymmetry and circularity. In…
In this talk I will briefly outline work in progress in two different contexts in astrophysical relativity, i.e. the study of rotating star spacetimes and the problem of reliably extracting gravitational wave templates in numerical…
We develop a relativistic treatment of interference between light reflected from a falling cube retroreflector in the vertical arm of an interferometer, and light in a reference beam in the horizontal arm. Coordinates that are nearly…
We present a formulation of Regge Calculus where arbitrary coordinates are associated to each vertex of a simplicial complex and the degrees of freedom are given by the metric on each simplex. The lengths of the edges are thus determined…
I review recent developments in numerical relativity, focussing on progress made in 3D black hole evolution. Progress in development of black hole initial data, apparent horizon boundary conditions, adaptive mesh refinement, and…
We apply the ``consistent discretization'' technique to the Regge action for (Euclidean and Lorentzian) general relativity in arbitrary number of dimensions. The result is a well defined canonical theory that is free of constraints and…
Observations of gravitational waves provide new opportunities to study our Universe. In particular, mergers of stellar black holes are the main targets of the current gravitational wave experiments. In order to make accurate predictions, it…
Strong gravity in the immediate vicinity of compact objects (e.g., black holes, neutron stars) necessitates inclusion of general relativistic effects. Traditionally, pseudo-Newtonian potential representation of gravity were favored to…
Area Regge calculus is a candidate theory of simplicial gravity, based on the Regge action with triangle areas as the dynamical variables. It is characterized by metric discontinuities and vanishing deficit angles. Area Regge calculus…