If a body moves with certain speed $v$ in a region of spacetime described by the metric $g_{μν}$;
the time dilation to translation in minkoswki metric is given by:
$t = \frac{t_0}{\sqrt{1 - \frac{v^2}{c^2}}}$
the gravitational time dilation is given by:
$t = \frac{ct_0}{\sqrt{\frac{dS^2_{g_{μν}}}{dt^{2}g_{μν}}}}$
Note: $v$ is the velocity which includes motion resulting from the interaction with gravitational field.
I have come to know that the combined time dilation is not obtained by any simple combination of the results. How is it obtained?
