Quasimodes and a lower bound on the uniform energy decay rate for Kerr–AdS spacetimes
Mar 24, 201334 pages
Published in:
- Anal.Part.Diff.Eq. 7 (2014) 5, 1057-1090
- Published: Sep 27, 2014
e-Print:
- 1303.5944 [gr-qc]
View in:
Citations per year
Abstract: (MSP)
We construct quasimodes for the Klein–Gordon equation on the black hole exterior ofKerr–AdS (anti- de Sitter) spacetimes. Such quasimodes are associated withtime-periodic approximate solutions of the Klein–Gordon equation and providenatural candidates to probe the decay of solutions on these backgrounds. They areconstructed as the solutions of a semiclassical nonlinear eigenvalue problem arisingafter separation of variables, with the (inverse of the) angular momentumplaying the role of the semiclassical parameter. Our construction results inexponentially small errors in the semiclassical parameter. This implies thatgeneral solutions to the Klein Gordon equation on Kerr–AdS cannot decayfaster than logarithmically. The latter result completes previous work bythe authors, where a logarithmic decay rate was established as an upperbound.- wave equation
- black holes
- decay estimates
- Kerr – anti-deSitter
References(39)
Figures(0)
- [1]
- [2]
- [3]
- [4]
- [5]
- [6]
- [7]
- [8]
- [9]
- [10]
- [11]
- [12]
- [13]
- [14]
- [15]
- [16]
- [17]
- [18]
- [19]
- [20]
- [21]
- [22]
- [23]
- [24]
- [25]