# Foliating spacetime

Gold Member

## Main Question or Discussion Point

Hi all,

On page 9 the author foliates spacetime into spatial hypersurfaces, $$\Sigma_t$$, labeled by a global time function, t.
for each point of $$\Sigma^t$$ there is a vector $$n_\mu$$ orthogonal to it
These vectors generate a flow on spacetime.
Physically what are these curves? are they geodesics?
Have you links using his notations for the intrinsic metric?

thanks.

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