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_∗) ≤B. Buchdahl (1959 Phys. Rev. 116 1027) obtained the value B_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 Buchdahls bound to a lower value, B_BaHa = 3/8 (<4/9), by adding the dominant energy condition to Buchdahls assumptions. In this paper, we further decrease Barraco-Hamitys bound to B_new ≃ 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.