Related papers: Strichartz estimates on Kerr black hole background…
In this paper we analyze the perturbations of the Kerr-Newman dilatonic black hole background. For this purpose we perform a double expansion in both the background electric charge and the wave parameters of the relevant quantities in the…
We calculate analytically asymptotic values of quasi-normal frequencies of four-dimensional Kerr black holes by solving the Teukolsky wave equation. We obtain an expression for arbitrary spin of the wave in agreement with Hod's proposal…
We study the scattering of monochromatic bosonic plane waves impinging upon a rotating black hole, in the special case that the direction of incidence is aligned with the spin axis. We present accurate numerical results for electromagnetic…
General relativity (GR) predicts the existence of black hole (BH). The rotating BH called as a Kerr Black hole and GR implies that there is an upper limit on the angular momentum per mass squared of black holes $\leq 1$, above which the…
In this paper we focus on the global-in-time existence and the pointwise estimates of solutions to the initial value problem for the semilinear dissipative wave equation in multi-dimensions. By using the method of Green function combined…
We investigate the wave properties of the Kerr black hole with isothermal plasma using 3+1 ADM formalism. The corresponding Fourier analyzed perturbed GRMHD equations are used to obtain the dispersion relations. These relations lead to the…
We study the superradiant scattering of gravitational waves by a nearly extremal black hole (dimensionless spin $a=0.99$) by numerically solving the full Einstein field equations, thus including backreaction effects. This allows us to study…
In this paper we investigate a construction of scattering for wave-type equations with singular potentials on the whole space $\mathbb{R}^n$ in a framework of weak-$L^p$ spaces. First, we use an Yamazaki-type estimate for wave groups on…
The lack of a positive-definite and conserved energy is a serious obstacle in the black hole stability problem. In this work, we will show that there exists a positive-definite and conserved Hamiltonian energy for axially symmetric linear…
The quest for extension of holographic correspondence to the case of finite temperature naturally includes Kerr-AdS black holes and their field theory duals. We probe the five-dimensional Kerr-AdS space time by pulsating strings. First we…
We establish an exponential decay estimate for linear waves on the Kerr-de Sitter slowly rotating black hole. Combining the cutoff resolvent estimate of arXiv:1003.6128 with the red-shift effect and a parametrix near the event horizons, we…
The Teukolsky equation describing scattering from Kerr black holes captures a few important effects in the process of binary mergers, such as tidal deformations and the decay of ringdown modes, thereby raising interest in the structure of…
This paper aims to give a general (possibly compact or noncompact) analog of Strichartz inequalities with loss of derivatives, obtained by Burq, G\'erard, and Tzvetkov [19] and Staffilani and Tataru [51]. Moreover we present a new approach,…
Characterizing distinct electron wave packets is a basic task for solid-state electron quantum optics with applications in quantum metrology and sensing. A important circuit element for this task is a non-stationary potential barrier than…
We study a massless scalar field propagating in the background of a five-dimensional rotating black hole. We showed that in the Myers-Perry metric describing such a black hole the massless field equation allows the separation of variables.…
In this article we prove a family of local (in time) weighted Strichartz estimates with derivative losses for the Klein-Gordon equation on asymptotically de Sitter spaces and provide a heuristic argument for the non-existence of a global…
A refinement of the energy method is introduced for dispersive PDE with derivative nonlinearity posed on tori. Key ingredient is a shorttime bilinear Strichartz estimate, which is used in a known combination of perturbative and energy…
In this article we study the pointwise decay properties of solutions to the wave equation on a class of nonstationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form…
We study the dispersive behaviors of two-particles Schr\"odinger and wave equations in the Aharonov-Bohm field. In particular, we prove the Strichartz estimates for Schr\"odinger and wave equations in this setting. The key point is to…
We prove resolvent estimates for a Schr\"odinger operator with a short-range potential outside an obstacle with Dirichlet boundary conditions. As a consequence, we deduce integrability of the local energy for the wave equation, and…