Strichartz Estimates on Schwarzschild Black Hole Backgrounds

By Jeremy Louis Marzuola, Jason Metcalfe, D. Tataru, Mihai Tohaneanu. 2008

139 citations recorded by the source corpus.

We study dispersive properties for the wave equation in the Schwarzschild space-time. The first result we obtain is a local energy estimate. This is then used, following the spirit of [29], to establish global-in-time Strichartz estimates. A considerable part of the paper is devoted to a precise analysis of solutions near the trapping region, namely the photon sphere.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f1643227dbf05109900595eda710f5b5c27cc7d9

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In Applied Mathematics

In Astronomy and Astrophysics

In Mathematical Physics

Citations in the corpus

The global non-linear stability of the Kerr-de Sitter family of black holes (2016, background): “precise polynomial decay rates, for slowly rotating Kerr spacetimes, and Marzuola, Metcalfe, Tataru and Tohaneanu obtained Strichartz estimates [104], [137].”
A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds (2008, methodology): “An alternative proof of such estimates not relying on spherical harmonic decompositions is provided by our more recent [20], and independently, by the subsequent Marzuola et al. [ 41 ], where further important refinements are given, including applications to Strichartz estimates and nonlinear wave e”
Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov) (2010, result): “(There was also recent work by Marzuola, Metcalf, Tataru and Tohaneanu [36] on Strichartz estimates, and by Donninger, Schlag and Soffer [18] on L∞ estimates on Schwarzschild black holes, following L∞ estimates of Dafermos and Rodnianski [12, 10], of Blue and Soffer [4] on non-rotating charged black”
Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations I (2011, methodology): “Refinements for Schwarzschild were achieved in [23] and [39].”
Price's Law on Nonstationary Space-Times (2011, unknown): “it is known to hold for Schwarzschild (see [24] and [45]) as well as for Kerr with small angular momentum (see [29], [23], [66]) and for a class of small stationary perturbations of Schwarzschild (see [23]).”
Hidden symmetries and decay for the wave equation on the Kerr spacetime (2009, methodology): “These were extended to Strichartz estimates for the wave equation [37] and to decay estimates for Maxwell’s equation [6] and for Einstein’s equation on ultimately Schwarzschildean spacetimes [30].”
Stability and Instability of Extreme Reissner–Nordström Black Hole Spacetimes for Linear Scalar Perturbations II (2011, methodology): “aptures in a stable manner the so-called redshift eect, which allowed the authors to obtain quantitative pointwise estimates on the horizon H+. Renements for Schwarzschild were achieved in [23] and [39]. Similar estimates to [7] were derived in [9] for the whole parameter range of Reissner-Nordstrom”
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].”