Related papers: Strichartz estimates on Kerr black hole background…
The gravitational waves and energy radiations from a spinning compact object with stellar mass in a circular orbit in the equatorial plane of a supermassive Kerr black hole are investigated in this paper. The effect how the spin acts on…
The Helmholtz equation in one dimension, which describes the propagation of electromagnetic waves in effectively one-dimensional systems, is equivalent to the time-independent Schr\"odinger equation. The fact that the potential term…
Water waves are well-known to be dispersive at the linearization level. Considering the fully nonlinear systems, we prove for reasonably smooth solutions the optimal Strichartz estimates for pure gravity waves and the semi-classical…
The metrics of gravitational shock waves for a Schwarzschild black hole in ordinary coordinates and for a Kerr black hole in Boyer-Lindquist coordinates are derived. The Kerr metric is discussed for two cases: the case of a Kerr black hole…
The quasilocal energy associated with a constant stationary time slice of the Kerr spacetime is presented. The calculations are based on a recent proposal \cite{by} in which quasilocal energy is derived from the Hamiltonian of spatially…
In the presence of a rotating Kerr black hole, we investigate hydrodynamics of the massive particles and massless photons, to construct relations among number density, pressure and internal energy density of the massive particles and…
We provide a rigorous derivation of the precise late-time asymptotics for solutions to the scalar wave equation on subextremal Kerr backgrounds, including the asymptotics for projections to angular frequencies $\ell\geq 1$ and $\ell\geq 2$.…
It is shown that the generalized discrete nonlinear Schr\"odinger equation can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or the fifth-order KdV equations, depending on values of the parameters. In dispersionless…
Understanding the behaviour of linear waves on black hole backgrounds is a central problem in general relativity, intimately connected with the nonlinear stability of the black hole spacetimes themselves as solutions to the Einstein…
A pair of simple wave equations is presented for the symmetric gravitational and electromagnetic perturbations of a charged black hole. One of the equations is uncoupled, and the other has a source term given by the solution of the first…
We prove Strichartz estimates for solutions to Maxwell equations in three dimensions with rough permittivities, which have less than three different eigenvalues. To this end, Maxwell equations are conjugated to half-wave equations in phase…
We prove global Strichartz estimates without loss for the wave equation outside two strictly convex obstacles, following the roadmap introduced in [Lafontaine, 2017] for the Schr\"odinger equation. Moreover, we show a first step toward the…
We solve the elliptic equations associated with the Hamiltonian and momentum constraints, corresponding to a system composed of two black holes with arbitrary linear and angular momentum. These new solutions are based on a Kerr-Schild…
Phase space method provides a novel way for deducing qualitative features of nonlinear differential equations without actually solving them. The method is applied here for analyzing stability of circular orbits of test particles in various…
This note surveys how energy generation and strengthening has been used to prove Morawetz estimates for various field equations in Minkowski space, the exterior of the Schwarzschild spacetime, and the exterior of the Kerr spacetime. It…
We propose a simple approach for the radiative evolution of generic orbits around a Kerr black hole. For a scalar-field, we recover the standard results for the evolution of the energy $E$ and the azimuthal angular momentum $L_z$ . In…
General relativity makes clear predictions about the spacetime geometry around black holes. In the near future, new facilities will have the capability to explore the metric around SgrA$^*$, the supermassive black hole candidate at the…
We study extreme mass ratio inspirals occurring in modified gravity, for which the system is modeled by a small compact object with scalar charge spiraling into a supermassive Kerr black hole. Besides the tensorial gravitational waves…
Superradiant scattering of linear spin $s=0,\pm 1,\pm 2$ fields on Kerr black hole background is investigated in the time domain by integrating numerically the homogeneous Teukolsky master equation. The applied numerical setup has already…
We present a new method designed to avoid numerical challenges that have impeded calculation of the Lorenz gauge self-force acting on a compact object inspiraling into a Kerr black hole. This type of calculation is valuable in creating…