Supplemental material to: "The Spherically Symmetric Vacuum in Covariant F(T) Gravity Theory" by Andrew DeBenedictis and Saša Ilijić [https://arxiv.org/abs/1609.07465, to be published in Phys.Rev.D]
We provide the Mathematica notebook tetradTest.nb (PDF-printout: tetradTest.pdf) that can be used to study the properties of user supplied tetrads in the context of torsion-based gravity theories. In particular, the notebook computes the spin connection and the complete suite of torsion-related tensors including the torsion scalar T, with and without the use of the spin-connection. It then constructs the left hand side of the equation of motion of both the non-Lorentz-covariant and the Lorentz-covariant version of the F(T) theory of gravity (see [1510.08432]).
As the example we used the simple diagonal tetrad compatible with static spherical symmetry. It gives nonvanishing spin connection and within non-covariant F(T) it leads to non-diagonal left-hand-side of equation of motion that is incompatible with the diagonal energy-momentum tensor of static spherical symmetry. Within the covariant F(T) one obtains diagonal left-hand-side of equations of motion.
Last update Nov. 24. 2016.