OK, I realize I am probably on a hiding to nothing here, but please bear with me for now, I have tested my calculations so carefully that I am totally convinced that I have found an error in two published accounts of the BL line element . . . The first is Visser, equation (57) http://arxiv.org/abs/0706.0622 The second is a document by someone (possibly) with initials "ELR" Chapter 7: The Kerr Metric – Rotation and Rotating Black Holes: pisces.as.utexas.edu/GenRel/KerrMetric.pdf [Broken] Basically, in both cases the sign of the dt dPhi cross term is given as negative, but I can only get sensible answers with a positive term (changing no other signs in the line element). In my defence, I should explain that I am doing a full 4D geodesic simulation in GNU Octave, using BL coordinates to set initial conditions by specifying L and E, noting the 4-velocity norm is exactly -1.0, then converting to Doran coordinates for the integration, noting absolute rock-solid constancy of conserved energy, momentum, and of course the 4-velocity norm is absolutely stable at -1.0 at all times. To reiterate, this all happens with my positive signed cross term, if I change it back to the (supposedly correct) negative value, all the 4-velocity norms are off, and of course the trajectory is completely different. So, is anyone here able to check the validity of the two references above? I can of course give more information as required, but I think this is plenty for now.