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The Poincare half-plane model for hyperbolic space puts the following metric on the plane:
ds2=1y2(dx2+dy2).ds^2 = \frac{1}{y^2} (dx^2 + dy^2).ds2=y21(dx2+dy2).
Compute the Ricci scalar RRR for this metric in matrix form. Is this a vacuum solution to Einstein's equations?
Give your answer as an (R,(R,(R, Yes/No))) pair.
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