- qc / 0 50 40 47 v 4 6 M ar 2 00 8 Decay of Solutions of the Wave Equation in the Kerr Geometry
نویسندگان
چکیده
We consider the Cauchy problem for the massless scalar wave equation in the Kerr geometry for smooth initial data compactly supported outside the event horizon. We prove that the solutions decay in time in L ∞ loc. The proof is based on a representation of the solution as an infinite sum over the angular momentum modes, each of which is an integral of the energy variable ω on the real line. This integral representation involves solutions of the radial and angular ODEs which arise in the separation of variables.
منابع مشابه
ar X iv : g r - qc / 0 50 40 47 v 2 2 2 A ug 2 00 5 Decay of Solutions of the Wave Equation in the Kerr Geometry
We consider the Cauchy problem for the massless scalar wave equation in the Kerr geometry for smooth initial data supported outside the event horizon. We prove that the solutions decay in time in L ∞ loc. The proof is based on a representation of the solution as an infinite sum over the angular momentum modes, each of which is an integral of the energy variable ω on the real line. This integral...
متن کاملar X iv : g r - qc / 0 31 00 66 v 2 1 4 A ug 2 00 6 The wave equation on the Schwarzschild metric II : Local Decay for the spin 2 Regge Wheeler equation
Recently, it has been shown that the wave equation for a scalar field on the exterior part of the Schwarzschild manifold satisfies local decay estimates useful for scattering theory and global existence [2]. The extension for the linearized Einstein equation is considered here. In 1957, Regge and Wheeler investigated spin 2 tensor fields on the Schwarzschild manifold [4]. They classified such f...
متن کاملar X iv : g r - qc / 0 31 00 91 v 2 1 4 A ug 2 00 6 Semilinear wave equations on the Schwarzschild manifold I : Local Decay Estimates
The semilinear wave equation on the (outer) Schwarzschild manifold is studied. We prove local decay estimates for general (non-radial) data, deriving a-priori Morawetz type inequalities.
متن کاملar X iv : g r - qc / 0 31 00 66 v 1 1 4 O ct 2 00 3 The wave equation on the Schwarzschild metric II : Local Decay for the spin 2 Regge Wheeler equation
Recently, it has been shown that the wave equation for a scalar field on the exterior part of the Schwarzschild manifold satisfies local decay estimates useful for scattering theory and global existence [2]. The extension for the linearized Einstein equation is considered here. In 1957, Regge and Wheeler investigated spin 2 tensor fields on the Schwarzschild manifold [4]. They classified such f...
متن کاملar X iv : g r - qc / 0 20 30 83 v 1 2 4 M ar 2 00 2 A Geometrical Anisotropic Model of Space - time Based on Finslerian Metric
In this work we study an anisotropic model of general relativity based on the framework of Finsler geometry. The observed anisotropy of the microwave background radiation [8] is incorporated in the Finslerian structure of space-time. We also examine the electromagnetic (e.m.) field equations in our space. As a result a modified wave equation of e.m. waves yields.
متن کامل