Explore build-in tensor package in Maple.
As far as I know, it allows deal with tensors, their operations, and their use in General Relativity both in the natural basis and in a moving frame.
Also visit http://www.digi-area.com/DifferentialGeometryLibrary/. There are hundreds of exact...
http://digi-area.com/DifferentialGeometryLibrary/ includes over 580 objects for differential geometry and its applications. Moreover here is 380 Exact Solutions of Einstein's Field Equations. The formulas are represented in different forms: metric from, Contravariant Newman–Penrose Tetrad...