Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2003-09-10
Class.Quant.Grav. 21 (2004) 1559-1581
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
22 pages, no figures, final version accepted for publication in Class. Quantum Grav. The treatment of the junction conditions
Scientific paper
10.1088/0264-9381/21/6/018
We study radial perturbations of general relativistic stars with elastic matter sources. We find that these perturbations are governed by a second order differential equation which, along with the boundary conditions, defines a Sturm-Liouville type problem that determines the eigenfrequencies. Although some complications arise compared to the perfect fluid case, leading us to consider a generalisation of the standard form of the Sturm-Liouville equation, the main results of Sturm-Liouville theory remain unaltered. As an important consequence we conclude that the mass-radius curve for a one-parameter sequence of regular equilibrium models belonging to some particular equation of state can be used in the same well-known way as in the perfect fluid case, at least if the energy density and the tangential pressure of the background solutions are continuous. In particular we find that the fundamental mode frequency has a zero for the maximum mass stars of the models with solid crusts considered in Paper I of this series.
Karlovini Max
Samuelsson Lars
Zarroug Moundheur
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