Local energy estimate on Kerr black hole backgrounds

By D. Tataru, Mihai Tohaneanu. 2008

179 citations recorded by the source corpus.

We study dispersive properties for the wave equation in the Kerr space-time with small angular momentum. The main result of thispaper is to establish uniform energy bounds and local energy decay for such backgrounds.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/3415618d2da0628f450e3f719c32a8a8ea831f28

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Citations in the corpus

Hidden symmetries and decay for the wave equation on the Kerr spacetime (2009, methodology): “The key idea of [19, 49] is to start with such a function F , to replace the phase space coordinates for null geodesics by their conjugate Fourier or spectral variables, and to use the the resulting F in A.”
A new physical-space approach to decay for the wave equation with applications to black hole spacetimes (2009, unknown): “Schwarzschild, estimates of the form (i) are due to several authors (see Section 4.4.1 of [8]). For slowly rotating Kerr spacetimes (M,gM,a) with parameters SaS ≪ M, such estimates have been shown by [8, 17] (see also [2]), whereas, for the general sub-extremal Kerr case SaS < M, this will appear”
The linear stability of the Schwarzschild solution to gravitational perturbations (2016, background): “The analogous construction cannot, however, be done by a traditional vector field current; see [24, 1, 70] for the |a| ≪ M case and [26] for the full |a| < M case, where in addition to the hyperbolicity of trapping, the fact that trapped frequencies are not superradiant also plays an important role.”
The global non-linear stability of the Kerr-de Sitter family of black holes (2016, methodology): “After pioneering work by Wald [143] and Kay–Wald [87], Dafermos, Rodnianski and Shlapentokh–Rothman [42], [44] recently proved polynomial decay for the scalar wave equation on all (exact) subextremal Kerr spacetimes; Tataru and Tohaneanu [131], [132] proved Price’s law, i.”
Local decay of waves on asymptotically flat stationary space-times (2009, methodology): “The estimates in the Schwarzschild case are the end result of a series of papers by Laba-Soffer [28], Blue-Soffer [3, 4, 40], Blue-Sterbenz [5] DafermosRodnianski [16, 13] and Marzuola-Metcalfe-Tataru-Tohaneanu [31].”
Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| < M (2014, methodology): “Kerr case SaS ≪ Mwas ﬁrst proven in our [26], and subsequently, decay results have been established for SaS ≪ Min [27] and in the ﬁrst parts of this series [30], and independently by Tataru–Tohaneanu [63] and Andersson–Blue [3]. See also [49]. Our [30] also obtained such decay results in the general”