 The component of the acceleration vector normal to the surface is 

In a Schwarzschild coordinate system, for example, we find that 
as expected - we have simply re-derived the previous results presented in a frame-field in a coordinate basis.We define formula_10 so that in our Schwarzschild example formula_11.We can, if we desire, derive the accelerations ab and the adjusted "acceleration at infinity" ainfb from a scalar potential Z, though there is not necessarily any particular advantage in doing so.