81 citations · 432 across the 18 of their papers we have counts for
20 papers
Boundedness for the wave equation on stationary axisymmetric perturbations of Kerr
Yakov Shlapentokh-Rothman, Mihai Tohaneanu
On the full range of sub-extremal Kerr exterior spacetimes we give a new proof of energy boundedness for high-frequency projections of solutions to the wave equation onto trapped f…
Polynomial time decay for solutions of the Klein--Gordon equation on a subextremal Reissner--Nordström black hole
Yakov Shlapentokh-Rothman, Maxime Van de Moortel
We consider the massive scalar field equation on any subextremal Reissner--Nordström exterior metric . We prove that solutions with localized initi…
The asymptotics of massive fields on stationary spherically symmetric black holes for all angular momenta
Federico Pasqualotto, Yakov Shlapentokh-Rothman, Maxime Van de Moortel
We study the massive scalar field equation on a stationary and spherically symmetric black hole (including in particular the Schwarzschild and Reissner--Nords…
Boundedness and decay for the Teukolsky equation on Kerr in the full subextremal range : physical space analysis
Yakov Shlapentokh-Rothman, Rita Teixeira da Costa
This paper concludes the study, initiated by the authors in arXiv:2007.07211, of the Teukolsky equation of spin and spin on Kerr backgrounds in the full subextremal…
Twisted Self-Similarity and the Einstein Vacuum Equations
Yakov Shlapentokh-Rothman
In the previous works [I. Rodnianski and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution, arXiv:1912.08478 and Y. Shlapentokh-R…
Naked Singularities for the Einstein Vacuum Equations: The Interior Solution
Yakov Shlapentokh-Rothman
In a previous work [I. Rodnianski and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution, arXiv:1912.08478] we constructed solutio…
A scattering theory approach to Cauchy horizon instability and applications to mass inflation
Jonathan Luk, Sung-Jin Oh, Yakov Shlapentokh-Rothman
Motivated by the strong cosmic censorship conjecture, we study the linear scalar wave equation in the interior of subextremal strictly charged Reissner-Nordström black holes by ana…
Boundedness and decay for the Teukolsky equation on Kerr in the full subextremal range : frequency space analysis
Yakov Shlapentokh-Rothman, Rita Teixeira da Costa
This paper is the first of a series regarding the Teukolsky equation of spin and spin on Kerr backgrounds in the full subextremal range of parameters . In th…
Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution
Igor Rodnianski, Yakov Shlapentokh-Rothman
In this work we initiate the mathematical study of naked singularities for the Einstein vacuum equations in dimensions by constructing solutions which correspond to the exter…
Rough initial data and the strength of the blue-shift instability on cosmological black holes with
Mihalis Dafermos, Yakov Shlapentokh-Rothman
We consider the wave equation on Reissner-Nordström-de Sitter and more generally Kerr-Newman-de Sitter black hole spacetimes with . The strength of the blue-shift instability…
A scattering theory for linear waves on the interior of Reissner-Nordström black holes
Christoph Kehle, Yakov Shlapentokh-Rothman
We develop a scattering theory for the linear wave equation on the interior of Reissner-Nordström black holes, connecting the fixed frequency picture to the physical…
The Asymptotically Self-Similar Regime for the Einstein Vacuum Equations
Igor Rodnianski, Yakov Shlapentokh-Rothman
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 tec…
Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimes
Mihalis Dafermos, Yakov Shlapentokh-Rothman
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 celebrat…
Stationary axisymmetric black holes with matter
Otis Chodosh, Yakov Shlapentokh-Rothman
We provide a geometric framework for the construction of non-vacuum black holes whose metrics are stationary and axisymmetric. Under suitable assumptions we show that the Einstein…
Time-Periodic Einstein--Klein--Gordon Bifurcations of Kerr
Otis Chodosh, Yakov Shlapentokh-Rothman
We construct one-parameter families of solutions to the Einstein--Klein--Gordon equations bifurcating off the Kerr solution such that the underlying family of spacetimes are each a…
A scattering theory for the wave equation on Kerr black hole exteriors
Mihalis Dafermos, Igor Rodnianski, Yakov Shlapentokh-Rothman
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 re…
Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| < M
Mihalis Dafermos, Igor Rodnianski, Yakov Shlapentokh-Rothman
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 axisymmetr…
Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime
Yakov Shlapentokh-Rothman
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 appl…
Exponentially growing finite energy solutions for the Klein-Gordon equation on sub-extremal Kerr spacetimes
Yakov Shlapentokh-Rothman
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…
An Asymptotic Faber-Krahn Inequality for the Combinatorial Laplacian on Z^2
Yakov Shlapentokh-Rothman
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…