On the stability of a gaseous sphere against non-radial perturbations

Abstract : We present a simplified proof of the Antonov-Lebovitz theorem, asserting that any spherical barotropic star having a mass density decreasing monotonically outwards and vanishing at its surface is stable to all non-radial perturbations. We also develop a simple argument showing in a straightforward way a related but somewhat weaker result, according to which any such star is stable if and only if it is stable to radial perturbations. Extension of these results to a star with non-decreasing specific entropy distribution is also briefly discussed.
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Submitted on : Sunday, April 12, 2015 - 11:32:17 PM
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Jérôme Perez, Jean-Jacques Aly. On the stability of a gaseous sphere against non-radial perturbations. Monthly Notices of the Royal Astronomical Society, Oxford University Press (OUP): Policy P - Oxford Open Option A, 1992, 259 ((1)), pp 95-103. ⟨10.1093/mnras/259.1.95⟩. ⟨hal-01141417⟩

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