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There is a set of 16 polynomial curvature invariants called the Carminati-McLenaghan invariants, described here: https://en.wikipedia.org/wiki/Carminati–McLenaghan_invariants . They've been implemented (I think by Carminati and McLenaghan themselves) in a free Maple package described here: http://grtensor.phy.queensu.ca/Griihelp/cmscalar.help . Maple itself, however, is proprietary. I've implemented the CM invariants as open-source code https://github.com/bcrowell/cm_invariants that works in the open-source computer algebra system Maxima. I've written up a bunch of tests, e.g., calculating the invariants in spacetimes where I know that they should vanish, or spacetimes where I know that some of them should diverge at a curvature singularity. However, I haven't found any tabulations online of what the CM invariants are *supposed* to be in cases where they're finite. For example, there is an invariant called ##W_1##, and for the Schwarzschild spacetime I get ##W_1=6m^2/r^6##, but although this seems reasonable, I don't have any way to check whether it's right (e.g., whether the numerical coefficient should really be 6).
Would anyone who has a copy of Maple be willing to run the Maple implementation of the CM invariants and tell me some results that I could use to check whether my code is calculating correct output? The spacetimes that I have used so far for tests are in this test suite: https://github.com/bcrowell/cm_invariants/tree/master/tests .
Any help would be much appreciated!
Would anyone who has a copy of Maple be willing to run the Maple implementation of the CM invariants and tell me some results that I could use to check whether my code is calculating correct output? The spacetimes that I have used so far for tests are in this test suite: https://github.com/bcrowell/cm_invariants/tree/master/tests .
Any help would be much appreciated!