On the stability of axisymmetric systems to axisymmetric perturbations in general relativity. IV. Allowance for gravitational radiation in an odd-parity mode

Abstract

In the present paper, the variational principle derived in Paper II is clarified; and it is shown how it may be used to treat the damping of the axisymmetric oscillations of a uniformly rotating star, by the emission of gravitational radiation in an odd-parity mode. It is further shown that the expression, for the imaginary part of the frequency as a surface integral (at infinity), which follows from the variational principle, is consistent with the requirements of the conservation of energy.