Buchdahl's theorem gives for a static spherical perfect-fluid star whose density is nonincreasing outwards, subject to its regularity assumptions. Equality would require divergent central pressure, so every regular such star satisfies .
Buchdahl's theorem is a result in general relativity concerning the maximum mass of a spherical, isotropic, perfect fluid star in equilibrium. Specifically, the theorem states that the maximum ratio of a star's mass \( M \) to its radius \( R \) is constrained by: \[ \frac{M}{R} \leq \frac{4}{9} \] when measured in geometrized units (where \( G = c = 1 \)).
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