Riemann Normal Coordinate expansions using Cadabra

Abstract

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-order in the curvature and were obtained using the computer algebra package Cadabra.

v2: Updated to version 2 of Cadabra and fixed computational errors; v3: Corrected indices and sign on lhs of eqtns. 11.19a-d

References in corpus (3)

• A field-theory motivated approach to symbolic computer algebra
• A brief introduction to Cadabra: a tool for tensor computations in General Relativity
• A Smooth Lattice construction of the Oppenheimer-Snyder spacetime

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