Maximum mass of a barotropic spherical star

The ratio of total mass m(*) to the surface radius r(*) of a spherical perfect fluid ball has an upper bound, Gm(*)(c2r(*)) <= beta Buchdahl (1959 Phys. Rev. 116 1027) obtained the value beta(Buch) = 4/9 under the assumptions that the object has a nonincreasing mass density in the outward direction and a barotropic equation of state. Barraco and Hamity (2002 Phys. Rev. D 65 124028) decreased Buchdahl's bound to a lower value, beta(BaHa) - 3/8 (<4/9), by adding the dominant energy condition to Buchdahl's assumptions. In this paper, we further decrease Barraco-Hamity's bound to beta(new) similar or equal to 0.3636403 (<3/8) by adding the subluminal (slower than light) condition of sound speed. In our analysis we numerically solve the Tolman-Oppenheimer-Volkoff equations, and the mass-to-radius ratio is maximized by variation of mass, radius and pressure inside the fluid ball as functions of mass density.