Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case aM|a|\ll M

Nov 21, 2017
84 pages
e-Print:

Citations per year

20172018201920202021024681012
Abstract: (arXiv)
We prove boundedness and polynomial decay statements for solutions of the spin ±2\pm2 Teukolsky equation on a Kerr exterior background with parameters satisfying aM|a|\ll M. The bounds are obtained by introducing generalisations of the higher order quantities PP and P\underline{P} used in our previous work on the linear stability of Schwarzschild. The existence of these quantities in the Schwarzschild case is related to the transformation theory of Chandrasekhar. In a followup paper, we shall extend this result to the general sub-extremal range of parameters a<M|a|<M. As in the Schwarzschild case, these bounds provide the first step in proving the full linear stability of the Kerr metric to gravitational perturbations.
Note:
  • 84 pages, 3 figures