The Gravitational Perturbations of the Kerr Black Hole. II. The Perturbations in the Quantities which are Finite in the Stationary State
Abstract
The present paper completes the integration of the linearized Newman-Penrose equations governing the gravitational perturbations of the Kerr black hole. The equations which determine the solutions are the four (complex) Bianchi identities (not used in part I) and the 24 equations which follow from the commutation relations. The principal results are (1) the demonstration that the perturbation in the Weyl scalar Psi 2 must vanish in a gauge in which the scalars Psi 1 and Psi 3 are assumed to vanish identically; (2) the determination of the relative normalization of the radial functions (left unspecified in part I) through an integrability condition. Further, the solution to the integrability condition defines a function involving quadratures over Teukolsky's radial and angular functions; and it is in terms of this function that the perturbations in the metric coefficients are determined.
- Publication:
-
Proceedings of the Royal Society of London Series A
- Pub Date:
- January 1978
- DOI:
- 10.1098/rspa.1978.0021
- Bibcode:
- 1978RSPSA.358..441C