Maximum mass of a barotropic spherical star
Abstract
The ratio of total mass M to surface radius R of spherical perfect fluid ball has an upper bound, M/R < B. Buchdahl obtained B = 4/9 under the assumptions; non-increasing mass density in outward direction, and barotropic equation of states. Barraco and Hamity decreased the Buchdahl's bound to a lower value B = 3/8 (< 4/9) by adding the dominant energy condition to Buchdahl's assumptions. In this paper, we further decrease the Barraco-Hamity's bound to B 0.3636403 (< 3/8) by adding the subluminal (slower-than-light) condition of sound speed. In our analysis, we solve numerically 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.