= Tolman wormhole
{c}
{title2=$ds^2=(1+\lambda/r^2)^2\delta_{ij}dx^idx^j$}
For $\lambda>0$, this four-dimensional Euclidean metric has two asymptotically flat ends. Inversion $\rho=\lambda/r$ puts the metric near the $r=0$ end into the same form with $\rho\to\infty$. On $r>0$, its <Ricci scalar> vanishes because $\Delta(r^{-2})=0$, but its <Ricci tensor> is $R_{ij}=4\lambda(\delta_{ij}-4x_ix_j/r^2)/(r^2+\lambda)^2$. It therefore does not satisfy the <Vacuum Einstein equations> unless $\lambda=0$. For negative $\lambda$ the conformal factor vanishes at a finite radius, so that metric is not a smooth wormhole across that sphere.
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