A Hyperbolic Metric
Classical Mechanics
Level
3
The Poincare half-plane model for hyperbolic space puts the following metric on the plane:
\[ds^2 = \frac{1}{y^2} (dx^2 + dy^2).\]
Compute the Ricci scalar \(R\) for this metric in matrix form. Is this a vacuum solution to Einstein's equations? Give your answer as an (R, Yes/No) pair.
by
Matt DeCross