Bounds on 2m/R for static spherical objects

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Guven, Jemal
Ó Murchadha, Niall
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It is well known that a spherically symmetric constant density static star, modeled as a perfect fluid, possesses a bound on its mass m by its radial size R given by 2m/R less than or equal to 8/9 and that this bound continues to hold when the energy density decreases monotonically. The existence of such a bound is intriguing because it occurs well before the appearance of an apparent horizon at m = R/2. However, the assumptions made are extremely restrictive. They do not hold in a simple soap bubble and they certainly do not approximate any known topologically stable field configuration. In addition, Such configurations will not generally be compact. We show that the 8/9 bound is robust by relaxing these assumptions. If the density is monotonically decreasing and the tangential stress is less than or equal to the radial stress we show that the 8/9 bound continues to hold through the entire bulk if m is replaced by the quasi-local mass. If the tangential stress is allowed to exceed the radial stress and/or the density is not monotonic we cannot recover the 8/9 bound. However, we can show that 2m/R remains strictly bounded away from unity by constructing an explicit upper bound which depends only on the ratio of the stresses and the variation of the density. (S0556-2821(99)09818-5).
Classical general-relativity , Stellar models , Configuration-space , Symmetry , Constraints
Guven, J. and Ó Murchadha, N. (1999) 'Bounds on 2m/R for static spherical objects', Physical Review D, 60(8), 084020 (8pp). doi: 10.1103/PhysRevD.60.084020
© 1999, American Physical Society