Proper Time in Higher-Dim. Gravity: GR to HD

[center o bass]

In GR one of the fundamental postulates is that $-ds^2 = - g_{\mu \nu} dx^\mu dx^\nu$ is interpreted as a the time on the clock of an observer of constant spatial coordinates; a comoving observer. How does this translate to higher dimensional theories of gravity? There one has a higher dimensional metric $d\sigma^2 = G_{ab} dx^a dx^b$ which has $-ds^2$ contained within it. Do we still interpret $d\sigma^2$ as a the clock of a comoving observer?

 

[dauto]

Sure