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In this paper we used the theory of adiabatic radial oscillations developed by Chandrasekhar to study the conditions for dynamical stability of constant energy-density stars, or Schwarzschild stars, in the unstudied ultra compact regime beyond the Buchdahl limit, that is, for configurations with radius $R$ in the range $R_{\rm S}<R<(9/8)R_{\rm S}$, where $R_{\rm S}$ is the Schwarzschild radius of the star.
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