An infinite class of exact static anisotropic spheres that break the Buchdal bound

Abstract: An infinite class of exact static anisotropic spheres is developed. All members of the class satisfy (i) regularity (meaning no singularities), and in particular at the origin, (ii) positive but monotone decreasing energy density ($\rho(r)$), radial pressure ($p(r)$), and tangential pressure ($P(r)$), (iii) a finite value of $r=R$ such that $p(R)=0$ defining the boundary surface onto vacuum, (iv) $p \leq \rho$, and (v) $p + 2 P=3 \rho$. All standard energy conditions are satisfied except for the dominant energy condition which has an innocuous violation by the tangential stress since $\rho \leq P$ by construction. An infinite number of the solutions violate the Buchdal bound.