Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1999-03-17
Phys.Rev. D60 (1999) 084020
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
16 pages, Revtex
Scientific paper
10.1103/PhysRevD.60.084020
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 \le 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 humble soap bubble and they certainly do not approximate any known topologically stable field configuration. 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 exceeds 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.
Guven Jemal
Murchadha Niall O'
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