GRTensorII is a
Maple
''Acer'' is a genus of trees and shrubs commonly known as maples. The genus is placed in the soapberry family Sapindaceae.Stevens, P. F. (2001 onwards). Angiosperm Phylogeny Website. Version 9, June 2008 nd more or less continuously updated si ...
package designed for
tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other ...
computations, particularly in
general relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
.
This package was developed at
Queen's University in
Kingston
Kingston may refer to:
Places
* List of places called Kingston, including the six most populated:
** Kingston, Jamaica
** Kingston upon Hull, England
** City of Kingston, Victoria, Australia
** Kingston, Ontario, Canada
** Kingston upon Thames, ...
,
Ontario
Ontario is the southernmost Provinces and territories of Canada, province of Canada. Located in Central Canada, Ontario is the Population of Canada by province and territory, country's most populous province. As of the 2021 Canadian census, it ...
by Peter Musgrave, Denis Pollney and Kayll Lake. While there are many packages which perform tensor computations (including a ''standard Maple package''), GRTensorII is particularly well suited for carrying out routine computations of useful quantities when working with (or searching for)
exact solutions in general relativity
In general relativity, an exact solution is a (typically closed form) solution of the Einstein field equations whose derivation does not invoke simplifying approximations of the equations, though the starting point for that derivation may be a ...
. Its principal advantages include
*convenience of definition of new
spacetime
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...
s and tensor expression
*efficient computation with
frames
*efficient computation of Ricci and Weyl
spinor
In geometry and physics, spinors (pronounced "spinner" IPA ) are elements of a complex numbers, complex vector space that can be associated with Euclidean space. A spinor transforms linearly when the Euclidean space is subjected to a slight (infi ...
components and of
Petrov classification
*efficient computation of the
Carminati-McLenaghan invariants and other
curvature invariant
In Riemannian geometry and pseudo-Riemannian geometry, curvature invariants are scalar quantities constructed from tensors that represent curvature. These tensors are usually the Riemann tensor, the Weyl tensor, the Ricci tensor and tensors formed ...
s
Currently, GRTensorII does have some drawbacks:
*Maple is expensive
*valuable subpackages for perturbation and junction computations have not been updated
*no subpackage is yet publicly available in GRTensorII for executing the
Cartan-Karlhede algorithm
*sharing information with standard Maple packages can sometimes become awkward
References
* Not a textbook, but excellent supplementary reading. The author uses GRTensorII, so this book is particularly well suited for use by students who have a working installation of this package.
External links
GRTensorII home page{{Webarchive, url=http://webarchive.loc.gov/all/20020914105414/http%3A//grtensor.phy.queensu.ca/ , date=2002-09-14
General relativity