Traceless stress-energy and traversable wormholes

A one-parameter family of static and spherically symmetric solutions to Einstein equations with a traceless energy-momentum tensor is found. When the nonzero parameter $\beta$ lies in the open interval $(0,1)$ one obtains traversable Lorentzian wormholes. One also obtains naked singularities when either $\beta <0$ or $\beta >1$ and the Schwarzschild black hole for $\beta = 1$.