Related papers: Strichartz estimates on Schwarzschild black hole b…
We study the dispersive properties for the wave equation in the Kerr space-time with small angular momentum. The main result of this paper is to establish Strichartz estimates for solutions of the aforementioned equation. As an application,…
The localized energy estimate for the wave equation is known to be a fairly robust measure of dispersion. Recent analogs on the $(1+3)$-dimensional Schwarzschild space-time have played a key role in a number of subsequent results, including…
We study dispersive properties for the wave equation in the Kerr space-time with small angular momentum. The main result of thispaper is to establish uniform energy bounds and local energy decay for such backgrounds.
We study scattering of waves by black holes. Solving a massless scalar field with a point source in the Schwarzschild spacetime, waves scattered by the black hole is obtained numerically. We then reconstruct images of the black hole from…
We analyze the allowed energy levels of Hawking radiation from Schwarzschild surfaces in space-times with large extra dimensions. From the requirement that the wave functions associated with these particles be single-valued and obey radial…
The Schwarzschild spacetime is for electromagnetic waves like a nonuniform medium with a varying refraction index. A fraction of an outgoing radiation scatters off the curvature of the geometry and can be intercepted by a gravitational…
In this paper we study Strichartz estimates for dispersive equations which are defined by radially symmetric pseudo-differential operators, and of which initial data belongs to spaces of Sobolev type defined in spherical coordinates. We…
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…
In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.
We examine solutions to semilinear wave equations on black hole backgrounds and give a proof of an analog of the Strauss conjecture on the Schwarzschild and Kerr, with small angular momentum, black hole backgrounds. The key estimates are a…
We provide a uniform decay estimate of Morawetz type for the local energy of general solutions to the inhomogeneous wave equation on a Schwarzchild background. This estimate is both uniform in space and time, so in particular it implies a…
Approximative analytic solutions of the Dirac equation in the geometry of Schwarzschild black holes are derived obtaining information about the discrete energy levels and the asymptotic behavior of the energy eigenspinors.
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 employ the method of comparison equations to study the propagation of a massless minimally coupled scalar field on the Schwarzschild background. In particular, we show that this method allows us to obtain explicit approximate expressions…
We prove local in time Strichartz estimates for the Dirac equation on spherically symmetric manifolds. As an application, we give a result of local well-posedness for some nonlinear models.
We prove localized energy estimates for the wave equation in domains with a strictly concave boundary when homogeneous Dirichlet or Neumann conditions are imposed. By restricting the solution to small, frequency dependent, space time…
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…
We investigate the wave optics in spherically symmetric spacetimes: Schwarzschild black hole, spherical star with a perfect absorbing surface, and massless/massive Ellis wormholes. Assuming a point wave source, wave pattern and power…
We study thermodynamic evaporation of Schwarzschild-de Sitter black holes in terms of a low energy perturbation theory. A small black hole which is far from the cosmological horizon and observers at the spacelike hypersurface where black…
In this paper we present an exact solution of Einstein's field equations describing the Schwarzschild black hole in dark energy background. It is also regarded as an embedded solution that the Schwarzschild black hole is embedded into the…