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The Stability of Relativistic Systems

Published online by Cambridge University Press:  07 February 2017

S. Chandrasekhar
S. Chandrasekhar*
Affiliation:
University of Chicago, Chicago, Ill., U.S.A.

Abstract

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The stability of relativistic systems is reviewed against the background of what is known in the corresponding contexts of the Newtonian theory. In particular, the importance of determining whether Dedekind-like points of bifurcation occur along given stationary axisymmetric sequences is emphasized: the occurrence of such points of bifurcation may signal the onset of secular instability induced by radiation-reaction. (At a Dedekind-like point of bifurcation, the system can be subject, quasistationarily, to a non-axisymmetric deformation with an e2iϕ-dependence on the azimuthal angle ϕ.)

A formalism is described in terms of which the normal modes of axisymmetric oscillation of axisymmetric systems can be determined. Specialized to neutral modes of oscillation the formalism provides an alternative proof of Carter's theorem and clarifies the minimal requirements for its validity. A parallel formalism is described for ascertaining whether an axisymmetric system can be subject to a quasi-stationary non-axisymmetric deformation. The possibility of applying this latter formalism to determining whether a Dedekind-like point of bifurcation occurs along the Kerr sequence is considered.

Type
Part II: Stability and Collapse
Information
Symposium - International Astronomical Union , Volume 64: Gravitational Radiation and Gravitational Collapse , 1974 , pp. 63 - 81
Copyright
Copyright © Reidel 1974 

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