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Curvature of the two-dimensional hyperbolic polar metric

For the curvature convention

R^{α}_{β γ δ} = \partial_{γ} Γ_{β δ}^{α} - \partial_{δ} Γ_{β γ}^{α} + Γ_{β δ}^{μ} Γ_{μ γ}^{α} - Γ_{β γ}^{μ} Γ_{μ δ}^{α},

the independent nonzero mixed components are

R^{r}_{ϕ r ϕ} = - sinh^{2} r, R^{ϕ}_{r ϕ r} = - 1,

and the Ricci scalar is

R = - 2/ a^{2}

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