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arXiv · 1503.01517

Maximum mass of a barotropic spherical star

Atsuhito Fujisawa·Hiromi Saida·Chul-Moon Yoo·Yasusada Nambu
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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.

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Atsuhito Fujisawa, Hiromi Saida, Chul-Moon Yoo, Yasusada Nambu. 2015-03-05. Maximum mass of a barotropic spherical star. https://doi.org/10.1088/0264-9381/32/21/215028

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