Thursday, February 1, 2018

spacetime - What is the curvature of this shape? Is it closed?


This is a follow up question to this issue. I have the following metric:ds2s=[14ϕ2T2]dT2ϕ2T4dΘ2ϕ2T4sin2ΘdΦ2

Where ϕ is a constant in units of km s2 (length per square time), Φ and Θ are 3D polar coordinates and T is time. What is the curvature of this space at time, T?


If I travel in a straight line in the space defined by this metric and travel long enough, will I end up back where I started (is it closed)?




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