PROCRUSTES: A computer algebra package for post-Newtonian calculations in General Relativity

Abstract

We report on a package of routines for the computer algebra system Maple which supports the explicit determination of the geometric quantities, field equations, equations of motion, and conserved quantities of General Relativity in the post-Newtonian approximation. The package structure is modular and allows for an easy modification by the user. The set of routines can be used to verify hand calculations or to generate the input for further numerical investigations. Program summary Title of the program:Procrustes Catalogue identifier:ADYH_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/ADYH_v1_0 Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Computers:Platforms supported by the Maple computer algebra system (program was written under Maple 8, but also tested with Maple 9, 9.5, 10) Operating systems under which the program has been tested:Linux, Unix, Windows XP Programming language used:Maple internal language Memory required to execute typical problem:Dependent on problem (small ∼ couple of MBytes, large ∼ several GBytes) Classification:1.5 Relativity and Gravitation, 5 Computer Algebra No. bits in a word:Dependent on Maple distribution (supports 32 bit and 64 bit platforms) No. of processors used:1 No. of lines in distributed program, including test data, etc.: 10 881 No. of bytes in distributed program, including test data, etc.:47 743 Distribution format:tar.gz Nature of the physical problem:The post-Newtonian approximation represents an approximative scheme frequently used in General Relativity in which the gravitational potential is expanded into a series in inverse powers of the speed of light. Depending on the desired approximation level the field equations and equations of motion have to be determined up to given orders in the speed of light. This usually requires large algebraic computations due to the geometrical quantities entering the field equations and equations of motion. Method of solution:Automated computation using computer algebra techniques. Program has modular structure and only makes use of basic features of Maple to guarantee maximum compatibility and to allow for rapid extensions/modifications by the user. Typical running time:Dependent on problem (small ∼ couple of minutes, large ∼ couple of hours). Restrictions on the complexity of the problem:Sufficient amount of memory is the limiting factor for these calculations. The structure of the program allows one to handle large scale problems in an iterative manner to minimize the amount of memory required.