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 $B\simeq 0.3636403$ $(<3/8)$ 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.

14pages, 3figures. Accepted for Publication in Class.Quant.Grav

References in corpus (4)

• Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre
• Gravastar Shadows
• Bounds on the mass-to-radius ratio for non-compact field configurations
• Static perfect fluid balls with given equation of state and cosmological constant

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