Is Buchdahl star a Virial star?

In this talk I would characterize Buchdahl star, (M/R = 4/9 or in general Phi(R)=4/9 by gravitational field energy lying in the exterior of the star being half of its mass (non-gravitational energy) while for black hole the two are equal. Could this characterization be looked upon as the Virial equilibrium condition; average kinetic energy being half of average potential energy? We would further expound upon this novel and insightful suggestion that Bichdahl star may indeed be the Virial star.