scholarly journals General variational principle for normal modes of rotating stars

1979 ◽  
Vol 232 ◽  
pp. 874 ◽  
Author(s):  
B. F. Schutz
Keyword(s):  
Variational Principle ◽  
Normal Modes ◽  
Rotating Stars

Rapidly rotating relativistic stars

1992 ◽  
Vol 340 (1658) ◽  
pp. 391-422 ◽  
Keyword(s):  
Neutron Stars ◽  
Numerical Models ◽  
Normal Modes ◽  
Rotating Stars ◽  
Relativistic Stars ◽  
Small Oscillations ◽  
Perfect Fluids ◽  
Upper Limits ◽  
Viscosity Limit

Within the last decade, significant progress has been made in modelling rotating stars in general relativity and in relating observable properties to the equation of state of matter at high density. A formalism describing rotating perfect fluids is presented and numerical models of neutron stars are briefly discussed, with emphasis on upper limits on mass and rotation. The equations governing small oscillations are reviewed, and a variational principle appropriate both to eulerian and lagrangian perturbations is obtained. This extends to relativity an eulerian principle used to find non-axisymmetric stability points for perfect fluids. A related eulerian approach has been recently used to obtain normal modes of rotating newtonian stars. The review concludes with an outline of this work and of the two types of instability that can restrict the range of neutron stars. In particular, current work shows that several kinds of effective viscosity limit the possible role of a non-axisymmetric instability driven by gravitational waves.

scholarly journals Higher Modes of Non-Radial Oscillations of Stars by Variational Methods

1967 ◽  
Vol 20 (4) ◽  
pp. 363 ◽  
Author(s):  
AL Andrew
Keyword(s):  
Variational Principle ◽  
Variational Methods ◽  
Massive Star ◽  
Ritz Method ◽  
Normal Modes ◽  
Radial Oscillation ◽  
Higher Modes ◽  
Coordinate Functions

The Ritz method is applied to a variational principle of Chandrasekhar to determine the normal modes of non-radial oscillation of a massive star. Although good results are obtained for the f-mode and the p-modes, it is shown that the method may fail to detect the g-modes. The effect of the choice of coordinate functions is considered.

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