Abstract
An exact solution of Einstein's equations for a static isentropic perfect fluid sphere is examined in detail. The analysis yields a strong indication that the model isstable with respect to infinitesimal radial pulsations. This means that the temperature is decreasing outwards. We prove that the adiabatic speed of sound is everywhere less than the speed of light if and only if the radius of the sphere is larger than 1.61 times its Schwarzschild radius. We further show that the strong energy condition is fulfilled everywhere if and only if the radius is larger than 1.76 times the Schwarzschild radius. The necessary and sufficient condition for the speed of sound to be decreasing outwards is given, and we find that this criterion is fulfilled if the fluid is causal. Taking the values of the pressure ρ and the density ρ to be somewhere given by the maximum values from Baymet al.'s equation of state, i.e., ρ0=5.1×1014 g cm−3 andp 0=7.4×1033 dyne cm−2, we find the maximum mass of the fluid sphere to be 2.5 solar masses.
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Dedicated to the memory of the late George Cunliffe McVittie (1904–1988).
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Knutsen, H. The physical properties of an analytic model for a relativistic star. Astrophys Space Sci 162, 315–336 (1989). https://doi.org/10.1007/BF00640746
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DOI: https://doi.org/10.1007/BF00640746