Related papers: Strichartz estimates on Kerr black hole background…
We prove that for axially symmetric linear gravitational perturbations of the extreme Kerr black hole there exists a positive definite and conserved energy. This provides a basic criteria for linear stability in axial symmetry. In the…
Localized energy estimates for the wave equation have been increasingly used to prove various other dispersive estimates. This article focuses on proving such localized energy estimates on $(1+4)$-dimensional Myers-Perry black hole…
We identify a set of Hertz potentials for solutions to the vector wave equation on black hole spacetimes. The Hertz potentials yield Lorenz gauge electromagnetic vector potentials that represent physical solutions to the Maxwell equations,…
We study the scattering of massless scalar waves by a Kerr black hole by letting plane monochromatic waves impinge on the black hole. We calculate the relevant scattering phase-shifts using the Pruefer phase-function method, which is…
Using the Kerr-Schild formalism to solve the Einstein-Maxwell equations, we study energy transport due to time-dependent electromagnetic perturbations around a Kerr black hole, which may work as a mechanism to illuminate a disk located on…
We study the order ten polynomial equation satisfied by the radius of the spherical timelike orbits for a massive particle with a generic energy around a Kerr black hole. Even though the radii of the prograde and retrograde orbits at the…
We compute the propagation and scattering of linear gravitational waves off a Schwarzschild black hole using a numerical code which solves a generalization of the Zerilli equation to a three dimensional cartesian coordinate system. Since…
We compute numerically the absorption cross section of planar massless scalar waves impinging upon a Kerr-Newman black hole with different incidence angles. We investigate the influence of the black hole electric charge and angular momentum…
We prove global existence, boundedness and decay for small data solutions $\psi$ to a general class of quasilinear wave equations on Kerr black hole backgrounds in the full sub-extremal range $|a|<M$. The method extends our previous…
This short paper derives the constant of motion of a scalar field in the gravitational field of a Kerr black hole which is associated to a Killing tensor of that space-time. In addition, there is found a related new symmetry operator S for…
We study the scattering of massive spin-half waves by a Schwarzschild black hole using analytical and numerical methods. We begin by extending a recent perturbation theory calculation to next order to obtain Born series for the differential…
Our aim in this work is to give some quantitative insight on the dispersive effects exhibited by solutions of a semiclassical Schr{\"o}dinger-type equation in R d. We describe quantitatively the localisation of the energy in a long-time…
We revisit the problem of scalar and electromagnetic waves impinging upon a Schwarzschild black hole from complex angular momentum techniques. We focus more particularly on the associated differential scattering cross sections. We derive an…
We consider the propagation of a generic scalar field around a rotating and charged black hole. Using the partial wave method, we find, numerically, the total and partial absorption cross sections for different incidence angles. We…
The Hamilton-Jacobi equation for test particles in the Kerr geometry is separable. Using action-angle variables, we establish several relations between various physical quantities that characterize bound timelike geodesic orbits around a…
The separated radial part of a massive complex scalar wave equation in the Kerr- Sen geometry is shown to satisfy the generalized spheroidal wave equation which is, in fact, a confluent Heun equation up to a multiplier. The Hawking…
We prove certain weighted Strichartz estimates and use these to prove a sharp theorem for global existence of small amplitude solutions of $\square u= |u|^p$, thus verifying the so-called "Strauss conjecture".
We obtain remarkably simple integral bounds for axially symmetric linear perturbations for the extreme Kerr black hole in terms of conserved energies. From these estimates we deduce pointwise bounds for the perturbations outside the…
Motivated by the recent introduction of the Dirac bracket framework to compute spinning observables for the scattering of Kerr black holes, we initiate the study of conserved quantities from an on-shell amplitude perspective. We establish…
We investigate the scattering of a massless scalar field by a Kerr-Newman black hole, considering the case of on-axis incidence. We use the partial wave method to find numerical results for the scattering cross section, which we compare…