Accretion limits the compactness of static stars

General relativity limits the compactness of static stars. If the pressure of the fluid is positive and the density decreases with distance from the center, the value of the circumferential radius of the star must be greater than (9/4) G M/c^2, or equivalently the redshift of the surface must be less than two. If constraints on the equation of state of the material are relaxed, general relativity alone does not restrict the redshift of a static stellar surface. However, because black hole candidates in the universe generally accrete material from their environs, the process of accretion provides upper limits on the redshift of a astrophysical black-hole candidates.