xPert: Computer algebra for metric perturbation theory

Abstract

We present the tensor computer algebra package xPert for fast construction and manipulation of the equations of metric perturbation theory, around arbitrary backgrounds. It is based on the combination of explicit combinatorial formulas for the n-th order perturbation of curvature tensors and their gauge changes, and the use of highly efficient techniques of index canonicalization, provided by the underlying tensor system xAct, for Mathematica. We give examples of use and show the efficiency of the system with timings plots: it is possible to handle orders n=4 or n=5 within seconds, or reach n=10 with timings below 1 hour.

11 pages, 4 figures. Package can be downloaded from http://metric.iem.csic.es/Martin-Garcia/xAct/xPert/

References in corpus (7)

• Predictions from an anisotropic inflationary era
• The Invar tensor package: Differential invariants of Riemann
• Second Order Quasi-Normal Mode of the Schwarzschild Black Hole
• Second and higher-order quasi-normal modes in binary black hole mergers
• Cosmic microwave background bispectrum on small angular scales
• High-order gauge-invariant perturbations of a spherical spacetime
• Gauge invariant Boltzmann equation and the fluid limit