Non-existence of dynamic perturbations of Schwarzschild with vanishing self-dual part
- 1 January 1986
- journal article
- research article
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 3 (1) , 55-63
- https://doi.org/10.1088/0264-9381/3/1/008
Abstract
A recent proposal of Ashtekar (to be published) for the canonical quantisation of gravity involves a new choice of a (complex) polarisation on the (real) phase space of general relativity. In order for the 'four-dimensional' version of Ashtekar's proposal to be viable, it is necessary that for an arbitrary (real) background solution there exist a sufficient number of (complex) solutions of the linearised Einstein equation with perturbed Weyl spinor having vanishing self-dual part. The author shows that this is not the case by explicitly demonstrating that for the Schwarzschild spacetime, aside from stationary perturbations there are now such linearised solutions which can be expressed as superpositions of modes of real frequencies. The viability of the '3+1 version' of Ashtekar's proposal is not affected by these considerations.This publication has 3 references indexed in Scilit:
- Geometric quantization and the Bogoliubov transformationProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1981
- Construction of Solutions of Gravitational, Electromagnetic, or Other Perturbation Equations from Solutions of Decoupled EquationsPhysical Review Letters, 1978
- On perturbations of a Kerr black holeJournal of Mathematical Physics, 1973