# centrifugal acceleration and circular velocity in curved space time

I'm studying a problem on rotation systems in general relativity. I would like to know how do these two well know newtonian formulas:

$$a_{c}(r)=\dfrac{V_{c}^{2}(r)}{r},\\-\:\dfrac{\partial\Phi(r)}{\partial r}\|_{z=0}=a_{c}(r)$$

where $a_{c}(r)$ is the centrifugal acceleration, $V_{c}(r)$ the circular velocity (in the $\theta=\pi/2$ plane) at a distance $r$ and $\phi(r)$ the gravitational potential, change for curved space times?

Let's say, a space-time with metric tensor $$ds^{2}=-e^{\nu(r)}dt^{2}+e^{\lambda(r)}dr^{2}+r^{2}(d\theta^{2}+\sin^{2}\theta d\phi^{2})$$

• I think you have the wrong tags. Try General Relativity instead of Newtonian... – ggcg Dec 19 '18 at 12:38