The t and z coordinates remain unchanged. In this new coordinate system, the incremental proper time equation is d τ τ = [ 1 − − ( r ω ω c ) 2 ] d t 2 − − d r 2 c 2 − − r 2 d θ θ 2 c 2 − − d z 2 c 2 − − 2 r 2 ω ω d t d θ θ c 2 .