Yakov Shlapentokh-Rothman

• Massachusetts Institute of Technology

We consider the wave equation on Reissner Nordstrom de Sitter and more generally Kerr Newman de Sitter black hole spacetimes with λ > 0. The strength of the blue-shift instability associated to the Cauchy horizon of these spacetimes has been the subject of much discussion, since-in contrast to the asymptotically flat λ = 0 case-the competition with...

We consider the wave equation on Reissner-Nordstr\"om-de Sitter and more generally Kerr-Newman-de Sitter black hole spacetimes with $\Lambda>0$. The strength of the blue-shift instability associated to the Cauchy horizon of these spacetimes has been the subject of much discussion, since-in contrast to the $\Lambda=0$ case-the competition with the d...

We develop a local theory for the construction of singular spacetimes in all spacetime dimensions which become asymptotically self-similar as the singularity is approached. The techniques developed also allow us to construct and classify exact self-similar solutions which correspond to the formal asymptotic expansions of Fefferman and Graham's ambi...

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 strong cosmic censorship conjecture) and the time-reversed red-shift at the event horizon (relevant in classical sc...

We develop a definitive physical-space scattering theory for the scalar wave equation on Kerr exterior backgrounds in the general subextremal case |a|<M. In particular, we prove results corresponding to "existence and uniqueness of scattering states" and "asymptotic completeness" and we show moreover that the resulting "scattering matrix" mapping r...

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 definitive boundedness and decay results for the scalar wave equation on Kerr backgrounds in the general subextremal...

We give a quantitative refinement and simple proofs of mode stability type statements for the wave equation on Kerr backgrounds in the full sub-extremal range (|a| < M). As an application, we are able to quantitatively control the energy flux along the horizon and null infinity and establish integrated local energy decay for solutions to the wave e...

For any sub-extremal Kerr spacetime with non-zero angular momentum, we find an open family of non-zero masses for which there exist smooth, finite energy, and exponentially growing solutions to the corresponding Klein-Gordon equation. If desired, for any non-zero integer m, an exponentially growing solution can be found with mass arbitrarily close...

The Faber-Krahn inequality states that among all open domains with a fixed volume in R^n, the ball minimizes the first Dirichlet eigenvalue of the Laplacian. We study an asymptotic discrete analogue of this for the combinatorial Dirichlet Laplacian acting on induced subgraphs of Z^2. Namely, an induced subgraph G with n vertices is called a minimiz...