Hi, I derived Raychaudhuri Equations in both (- + + +) and (+ - - -) sign conventions from metric. In Robert Wald and Sean Carroll books, (- + + +) sign convention and I derived correctly in that Sign Convention as given in the books. In the other convention, I am having one sign difference in Shear equation, because I changed the Sign in Projection Tensor (Pμν) to save some properties on the whole derivation is based. These are: - BμνUμ = 0 = BμνUν where Uμ is tangent vector field Similar properties exist for shear (σμν) and rotation (ωμν) To prove them, in (- + + +) convention Pμν = gμν + UμUνBut in (+ - - -) convention Pμν = gμν - UμUν Because of this, the Riemann part of Shear equation in (- + + +) convention is CταβμUμUν + ½Rαβ while in (+ - - -) comes up as CταβμUμUν - ½Rαβ where Rαβ is spatially projected trace-less part of Ricci. I am pretty sure about the reason why the sign change is occurring (that is the change of sign in Projection Tensor in which makes it look correct thing to happen) but another possibility is that maybe Weyl tensor (Cταβμ) has different signs under different conventions and I don't know about that. Please Help! Also what are "spatial" tensors?