Giulio Magli 1997 Class. Quantum Grav. 14 1937 doi:10.1088/0264-9381/14/7/026
Gravitational collapse with non-vanishing tangential stresses: a generalization of the Tolman - Bondi model
Giulio Magli
Show affiliationsThe gravitational dynamics of anisotropic elastic spheres supported only by tangential stresses and satisfying an equation of state is analysed, and a fairly large class of non-static, spherically symmetric solutions of the Einstein field equations is found by quadratures. The solutions contain three arbitrary functions. Two such functions are immediately recognized as the initial distributions of mass and energy, familiar from the Tolman - Bondi (dust) models, while the third is the elastic internal energy per unit volume. If this function is a constant, the energy density becomes proportional to the matter density and therefore the metric reduces to the Tolman - Bondi one. In the general case, however, the solutions contain oscillating models as well as finite-bouncing models.
- PACS
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04.40.Dg Relativistic stars: structure, stability, and oscillations
- MSC
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83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
83D05 Relativistic gravitational theories other than Einstein's, including asymmetric field theories
- Subjects
- Dates
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Issue 7 (July 1997)
Received 16 December 1996, in final form 21 March 1997
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Gravitational collapse with non-vanishing tangential stresses: a generalization of the Tolman - Bondi model
Giulio Magli 1997 Class. Quantum Grav. 14 1937
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