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On the possibility of general relativistic oscillations

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On the possibility of general relativistic oscillations ANNALES DE L’I. H. P., SECTION A H. KNUTSEN R. STABELL On the possibility of general relativistic oscillations Annales de l’I. H. P., section A, tome 31, no 4 (1979), p. 339-353. <http://www.numdam.org/item?id=AIHPA_1979__31_4_339_0> © Gauthier-Villars, 1979, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section A », implique l’accord avec les conditions générales d’utilisation (http://www. numdam.org/legal.php). Toute utilisation commerciale ou impression systé- matique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ p. 339 On the possibility of general relativistic oscillations H. KNUTSEN (*) R. STABELL Institute of Theoretical Astrophysics, Box 1029, University of Oslo, Norway. Ann. Inst. Henri Poincare , Vol. XXXI, nO 4, 1979, Section A: Physique , théorique. , ABSTRACT. A group of solutions of Einstein’s field equations for a spherically symmetric distribution of matter is investigated. If the mass is at rest at the initial moment and the pressure and density are both zero at the boundary (gas cloud or dust cloud with a density gradient defined everywhere), it is found that oscillations are not possible. If the density at the boundary is positive, it is shown that, for some classes of solutions, oscillations are not possible, whereas other classes of solutions satisfy necessary conditions for oscillatory motion. However, these conditions are in general not sufficient. INTRODUCTION In a series of papers G. C. MvVittie has investigated the radial motions of a spherically symmetric mass distribution under the influence of gravi- tation and its pressure gradient (McVittie, 1964, 1966 and 1967). By impos- ing certain symmetry conditions, instead of assuming a particular equ

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