Looking for static interior solutions of Buchdahl star with $p_r=0,p_t=k\rho$ in general relativity and pure Lovelock theories

We find static fluid solutions of Einstein and pure Lovelock equations with $p_r=0$, $p_t=k\rho$, which could be possible models for the interior of a Buchdahl-like star. Buchdahl star is a limiting stellar configuration without a horizon whose formation does not need any exotic matter.