71 citations · 236 across the 20 of their papers we have counts for
20 papers
Using Cadabra for tensor computations in General Relativity
Leo Brewin
Cadabra is an open access program ideally suited to complex tensor commutations in General Relativity. Tensor expressions are written in LaTeX while an enhanced version of Python i…
Evolutions of Gowdy, Brill and Teukolsky initial data on a smooth lattice
Leo Brewin
Numerical results, based on a lattice method for computational general relativity, will be presented for Cauchy evolution of initial data for the Brill, Teukolsky and polarised Gow…
Curvature corrected estimates for geodesic arc-length
Leo Brewin
We will develop simple relations between the arc-lengths of a pair of geodesics that share common end-points. The two geodesics differ only by the requirement that one is constrain…
Two dimensional axisymmetric smooth lattice Ricci flow
Leo Brewin
A lattice based method will be presented for numerical investigations of Ricci flow. The method will be applied to the particular case of 2-dimensional axially symmetric initial da…
A numerical study of the Regge Calculus and Smooth Lattice methods on a Kasner cosmology
Leo Brewin
Two lattice based methods for numerical relativity, the Regge Calculus and the Smooth Lattice Relativity, will be compared with respect to accuracy and computational speed in a ful…
An Einstein-Bianchi system for Smooth Lattice General Relativity. II. 3+1 vacuum spacetimes
Leo Brewin
We will present a complete set of equations, in the form of an Einstein-Bianchi system, that describe the evolution of generic smooth lattices in spacetime. All 20 independent Riem…
An Einstein-Bianchi system for Smooth Lattice General Relativity. I. The Schwarzschild spacetime
Leo Brewin
The second Bianchi identity can be recast as an evolution equation for the Riemann curvatures. Here we will report on such a system for a vacuum static spherically symmetric spacet…
Fast algorithms for computing defects and their derivatives in the Regge calculus
Leo Brewin
Any practical attempt to solve the Regge equations, these being a large system of non-linear algebraic equations, will almost certainly employ a Newton-Raphson like scheme. In such…
A Smooth Lattice construction of the Oppenheimer-Snyder spacetime
Leo Brewin, Jules Kajtar
We present test results for the smooth lattice method using an Oppenheimer-Snyder spacetime. The results are in excellent agreement with theory and numerical results from other aut…
A brief introduction to Cadabra: a tool for tensor computations in General Relativity
Leo Brewin
Cadabra is a powerful computer program for the manipulation of tensor equations. It was designed for use in high energy physics but its rich structure and ease of use lends itself…
Deriving the ADM 3+1 evolution equations from the second variation of arc length
Leo Brewin
We will show that the ADM 3+1 evolution equations, for a zero shift vector, arise naturally from the equations for the second variation of arc-length.
Riemann Normal Coordinate expansions using Cadabra
Leo Brewin
Riemann normal coordinate expansions of the metric and other geometrical quantities, including the geodesic arc-length, will be presented. All of the results are given to fifth-ord…
A simple expression for the ADM mass
Leo Brewin
We show by an almost elementary calculation that the ADM mass of an asymptotically flat space can be computed as a limit involving a rate of change of area of a closed 2-surface. T…
Classroom computer animations of relativistic objects
Leo Brewin
This is a short note to announce the availability of some movies that may be useful in classroom discussions on the photographic appearance of objects moving at relativistic speeds…
Long term stable integration of a maximally sliced Schwarzschild black hole using a smooth lattice method
Leo Brewin
We will present results of a numerical integration of a maximally sliced Schwarzschild black hole using a smooth lattice method. The results show no signs of any instability formin…
Stable evolution of a maximally sliced Schwarzschild spacetime using a smooth lattice
Leo Brewin
We will present results of a long term stable evolution, to , of a maximally sliced Schwarzschild blackhole using a smooth lattice method.
On the convergence of Regge calculus to general relativity
Leo C. Brewin, Adrian P. Gentle
Motivated by a recent study casting doubt on the correspondence between Regge calculus and general relativity in the continuum limit, we explore a mechanism by which the simplicial…
An ADM 3+1 formulation for Smooth Lattice General Relativity
Leo Brewin
A new hybrid scheme for numerical relativity will be presented. The scheme will employ a 3-dimensional spacelike lattice to record the 3-metric while using the standard 3+1 ADM equ…
Riemann Normal Coordinates, Smooth Lattices and Numerical Relativity
Leo Brewin
A new lattice based scheme for numerical relativity will be presented. The scheme uses the same data as would be used in the Regge calculus (eg. a set of leg lengths on a simplicia…
Is the Regge Calculus a consistent approximation to General Relativity?
Leo Brewin
We will ask the question of whether or not the Regge calculus (and two related simplicial formulations) is a consistent approximation to General Relativity. Our criteria will be ba…