Related papers: Sharp decay estimates for massless Dirac fields on…
We prove in this paper the linear stability of the celebrated Schwarzschild family of black holes in general relativity: Solutions to the linearisation of the Einstein vacuum equations around a Schwarzschild metric arising from regular…
Perturbations of the Dirac field in the Schwarzschild spacetime are characterized by two wave equations (for two chiralities) with effective potentials which are iso-spectral and one of which is positive definite. Therefore, the stability…
Consider a spherically symmetric spacetime generated by a self-gravitating massless scalar field $\phi$ and let $\psi$ be a test (nonspherical) massless scalar field propagating on this dynamical background. Gundlach, Price, and Pullin…
Using the Frobenius method, we find high overtones of the Dirac quasinormal spectrum for the Schwarzschild black hole. At high overtones, the spacing for imaginary part of $\omega_{n}$ is equidistant and equals to…
We show asymptotic completeness for linear massive Dirac fields on the Schwarzschild-Anti-de Sitter spacetime. The proof is based on a Mourre estimate. We also construct an asymptotic velocity for this field.
We investigate the power-law tails in the evolution of a charged massless scalar field around a fixed background of a dilaton black hole. Using both analytical and numerical methods we find the inverse power-law relaxation of charged fields…
We consider a spherically symmetric characteristic initial value problem for the Einstein-Maxwell-scalar field equations. On the initial outgoing characteristic, the data is assumed to satisfy the Price law decay widely believed to hold on…
We consider the Klein-Gordon equation on the exterior of the toric anti de-Sitter Schwarzschild black hole with Dirichlet, Neumann and Robin boundary conditions at $\mathcal{I}$. We define a non-degenerate energy for the equation which…
This is the second part of a series of papers deriving the precise, late-time behaviour and (in)stability properties of charged scalar fields on near-extremal Reissner--Nordstr\"om spacetimes via energy estimates. In this paper, we use…
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 consider solutions of the scalar wave equation $\Box_g\phi=0$, without symmetry, on fixed subextremal Reissner-Nordstr\"om backgrounds $({\mathcal M}, g)$ with nonvanishing charge. Previously, it has been shown that for $\phi$ arising…
In Schwarzschild spacetime, the gravitational spin-orbit couplings of the massless Dirac field and the photon field can be studied in a unified way. In contrary to the previous investigations presented mainly at the quantum-mechanical…
The decay behavior of a massless scalar field in the Schwarzschild-de Sitter spacetime is well-known to follow an exponential law at asymptotically late times $t \rightarrow \infty$. In contrast, a massive scalar field in the asymptotically…
In this paper, we study the long time dynamics of solutions to the defocusing semilinear wave equation $\Box_g\phi=|\phi|^{p-1}\phi$ on the Schwarzschild black hole spacetimes. For $\frac{1+\sqrt{17}}{2}<p<5$ and sufficiently smooth and…
We consider solutions of the massless scalar wave equation $\Box_g\psi=0$, without symmetry, on fixed subextremal Kerr backgrounds $(\mathcal M, g)$. It follows from previous analyses in the Kerr exterior that for solutions $\psi$ arising…
We investigate the asymptotic stability of solutions to the characteristic initial value problem for the Einstein (massless) scalar field system with a positive cosmological constant. We prescribe spherically symmetric initial data on a…
In this paper, we consider the Casimir energy of massless scalar field which satisfy Dirichlet boundary condition on a spherical shell. Outside the shell, the spacetime is assumed to be described by the Schwarzschild metric, while inside…
The Dirac equation is considered in Schwarzschild black hole immersed in an electromagnetic universe with charge coupling. The equations of the charged spin-1/2 particle is separated into radial and angular equations by adopting the…
We get decay rate of higher derivatives of nonlinear massless Dirac equations with a kind of "good" spin null form. The method we rely on is similar to that of Li and Zang. However, they only give the decay rate of solution itself to…
An algorithm for numerical computation of the barrier transparency for the potentials surrounding Schwarzschild black holes is described for massless spinor particles. It is then applied to calculate the all configurations (including the…