Let us define Boyer-Lindquist-type coordinates (rational polynomial version) on M, via the method chart(), the argument of which is a string expressing the coordinates names, their ranges (the default is (−∞,+∞)) and their LaTeX symbols:
The 4 parameters m, a, b and ℓ of the Kerr-AdS spacetime are declared as symbolic variables, a and b being the two angular momentum parameters and ℓ being related to the cosmological constant by Λ=−6ℓ2:
var('m a b',domain='real')
# Particular cases# m = 0# a = 0b=0# b = a
Some auxiliary functions:
keep_Delta=False# change to False to provide explicit expression for Delta_r, Xi_a, etc...