相关论文: A scattering theory for the wave equation on Kerr …

In this paper, we provide an elementary, unified treatment of two distinct blue-shift instabilities for the scalar wave equation on a fixed Kerr black hole background: the celebrated blue-shift at the Cauchy horizon (familiar from the…

We develop a scattering theory for the linear wave equation $\Box_g \psi = 0$ on the interior of Reissner-Nordstr\"om black holes, connecting the fixed frequency picture to the physical space picture. Our main result gives the existence,…

Motivated by the strong cosmic censorship conjecture, we study the linear scalar wave equation in the interior of subextremal strictly charged Reissner-Nordstr\"om black holes by analyzing a suitably-defined "scattering map" at $0$…

This paper concludes the series begun in [M. Dafermos and I. Rodnianski, Decay for solutions of the wave equation on Kerr exterior spacetimes I-II: the cases |a| << M or axisymmetry, arXiv:1010.5132], providing the complete proof of…

In this paper we generalise our previous results [1] concerning scattering on the exterior of collapsing dust clouds to the charged case, including in particular the extremal case. We analyse the energy boundedness of solutions $\phi$ to…

We consider solutions of the massless scalar wave equation $\Box_g\psi=0$, without symmetry, on fixed subextremal Kerr backgrounds $(\mathcal M, g)$. It follows from previous analyses in the Kerr exterior that for solutions $\psi$ arising…

We study scattering solutions $\phi$ of the linear wave equation on extremal Reissner-Nordstr\"{o}m spacetimes, satisfying the following properties: i) $\phi$ attains a prescribed radiation field $\psi_{\mathcal{I}}$ through future null…

In this paper we show that there is a breakdown of scattering between the event horizon (or the Cauchy horizon) and an intermediate Cauchy hypersurface in the dynamic interior of a Reissner-Nordstr\"om-like black hole. More precisely, we…

We present a general construction of semiglobal scattering solutions to quasilinear wave equations in a neighbourhood of spacelike infinity including past and future null infinity, where the scattering data are posed on an ingoing null cone…

It is known that sub-extremal black hole backgrounds do not admit a (bijective) non-degenerate scattering theory in the exterior region due to the fact that the redshift effect at the event horizon acts as an unstable blueshift mechanism in…

We study the Cauchy problem for the wave equation on extreme Kerr backgrounds under axisymmetry. Specifically, we consider regular axisymmetric initial data prescribed on a Cauchy hypersurface S which connects the future event horizon with…

In this paper we analyse the boundedness of solutions $\phi$ of the wave equation in the Oppenheimer--Snyder model of gravitational collapse in both the case of a reflective dust cloud and a permeating dust cloud. We then proceed to define…

We consider solutions of the scalar wave equation $\Box_g\phi=0$, without symmetry, on fixed subextremal Reissner-Nordstr\"om backgrounds $({\mathcal M}, g)$ with nonvanishing charge. Previously, it has been shown that for $\phi$ arising…

We prove that a large class of smooth solutions $\psi$ to the linear wave equation $\Box_g\psi=0$ on subextremal rotating Kerr spacetimes which are regular and decaying along the event horizon become singular at the Cauchy horizon. More…

In this paper, we study the focusing and defocusing energy--subcritical, nonlinear wave equation in $\mathbb{R}^{1+d}$ with radial initial data for $d = 4,5$. We prove that if a solution remains bounded in the critical space on its interval…

We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method we establish energy flux estimates on the light cone. Then by the characteristic…

This paper contains the first two parts (I-II) of a three-part series concerning the scalar wave equation \Box_g{\psi} = 0 on a fixed Kerr background. We here restrict to two cases: (II1) |a| \ll M, general {\psi} or (II2) |a| < M, {\psi}…

We prove scattering for the defocusing energy-critical non-linear wave equation with Dirichlet boundary conditions outside two strictly convex obstacles in dimension three. This is the first large data scattering result for such an equation…

We show that linear scalar waves are bounded and continuous up to the Cauchy horizon of Reissner-Nordstr\"om-de Sitter and Kerr-de Sitter spacetimes, and in fact decay exponentially fast to a constant along the Cauchy horizon. We obtain our…

We consider the stationary metrics that have both the black hole and the ergoregion. The class of such metric contains, in particular, the Kerr metric. We study the Cauchy problem with highly oscillatory initial data supported in a…