A recent question Rotation of our Galaxy's inertial frame is about an observational evidence of the space rotation. My question is if such a rotation is conceptually possible in GR. Can we assume that for whatever reason spacetime has evolved in such a way that an empty region of space now rotates relative to the universe? If so, what would be the evolution of this rotation in time? Would the rotation continue forever, stop instantly, or slow down gradually and how fast? Would this region expand or contract in the process?
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This is proof that $L'$ represents same equation of motion with $L$ through Lagrange eq. I understand $L'$ satisfies Lagrange eq, bu...
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