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

TL;DR

This paper introduces an infinite class of exact static anisotropic sphere solutions that satisfy most energy conditions but notably violate the Buchdal bound, challenging previous limits on compactness.

Contribution

It develops a new class of exact anisotropic sphere solutions that break the Buchdal bound while satisfying regularity and energy conditions.

Findings

Solutions violate the Buchdal bound.

All solutions satisfy regularity and energy conditions.

Tangential stress slightly violates dominant energy condition.

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.