  Time dilation $\frac{1}{\sqrt{1-v^2}}$ and relative velocity $v$ are
observationally indistinguishable in the special theory of relativity, a
duality that carries over into the general theory under Fermi coordinates along
a curve (in coordinate-independent language, in the tangent Minkowski space
along the curve). For example, on a clock stationary at radius $r$, a distant
observer sees time dilation of $\frac{1}{\sqrt{1-v^2}}=\frac{1}{\sqrt{1-2M/r}}$
under the Schwarzschild metric and sees the clock receding with a relative
velocity of $v=\sqrt{2M/r}$ under the Painlev{\'e}-Gullstrand free fall metric.
Duality implies that during gravitational collapse, the intensifying time
dilation observed at the star's center from a fixed radius $r>0$ is
indistinguishable (along a curve) from an increasing relative velocity at which
the center recedes as seen from any direction, implying a local inflation.
