Journal Article

Dipolar Oscillations of Stars in General Relativity

Masao Takata

in Publications of the Astronomical Society of Japan

Volume 60, issue 2, pages 245-258
Published in print April 2008 | ISSN: 0004-6264
Published online April 2008 | e-ISSN: 2053-051X | DOI: https://dx.doi.org/10.1093/pasj/60.2.245
Dipolar Oscillations of Stars in General Relativity

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  • Astrometry and Celestial Mechanics
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We present a concise second-order system of ordinary differential equations that describes the adiabatic dipolar oscillation of spherically-symmetric stars in general relativity. The derivation of the system is accomplished by formulating the equations as a Hamiltonian system, and reconsidering a known algebraic relation among the perturbed variables as an integral of the system. The new formulation allows us to examine the structure of eigenfunctions and properties of the eigenfrequency spectrum, so that we can establish a scheme to classify eigenmodes into p-modes and g-modes with mathematical rigorousness. We can also discuss the condition for the existence of dynamically-unstable modes. All of these analyses are totally analogous to those developed in the Newtonian case.

Keywords: relativistic processes; stars: neutron; stars: oscillations; stars: variables: general; methods: analytical

Journal Article.  10721 words. 

Subjects: Astrometry and Celestial Mechanics ; Astronomical Instrumentation, Methods, and Techniques ; Stars

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