Astronomy and Astrophysics – Astronomy
Scientific paper
Sep 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975phrvd..12.1526m&link_type=abstract
Physical Review D - Particles and Fields, 3rd Series, vol. 12, Sept. 15, 1975, p. 1526-1537.
Astronomy and Astrophysics
Astronomy
56
Black Holes (Astronomy), Invariance, Perturbation Theory, Astronomical Models, Canonical Forms, Space-Time Functions, Stellar Magnetic Fields, Transformations (Mathematics)
Scientific paper
We present the details of previously published results on the stability of the Reissner-Nordstrom family of black holes and discuss, in some detail, the reduction techniques which were used to simplify the perturbation problem. We develop the Hamiltonian formalism for the perturbations of an arbitrary static solution of the Einstein-Maxwell equations (with vanishing magnetic field) and show explicitly that the perturbed constraints are the generators of the coordinate and electromagnetic gauge transformations of the canonical perturbation variables. We show that the perturbed constraints have vanishing Poisson brackets with one another and use this result as the basis for our reduction technique. The canonical transformations which accomplish the reduction and the perturbation Hamiltonian are given explicitly for the Reissner-Nordstrom problem. We include a stability result for the (odd- and even-parity) L = 1 perturbations which were not previously considered.
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