- #1

Onyx

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- TL;DR Summary
- Why is the trace of the extrinsic curvature tensor negative?

Considering the FLWR metric in cartesian coordinates:

##ds^2=-dt^2+a^2(t)(dx^2+dy^2+dz^2)##

With ##a(t)=t##, the trace of the extrinsic curvature tensor is ##-3t##. But why is it negative if it's describing an expanding universe, not a contracting one?

##ds^2=-dt^2+a^2(t)(dx^2+dy^2+dz^2)##

With ##a(t)=t##, the trace of the extrinsic curvature tensor is ##-3t##. But why is it negative if it's describing an expanding universe, not a contracting one?