Related papers: Sharp decay estimates for massless Dirac fields on…
The aim of the present report is to study massless fermion perturbations outside five-dimensional stringy black holes with U(1) charges. The Dirac equation was numerically solved to obtain the time profiles for the evolving fermion fields,…
We investigate $L^1\to L^\infty$ dispersive estimates for the massless two dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies the natural $t^{-\frac12}$ decay rate, which may be improved…
Asymptotic analytic solutions of the Dirac equation, giving the scattering modes (of the continuous energy spectrum, $E>mc^2$) in Schwarzschild's chart and Cartesian gauge, are used for building the partial wave analysis of Dirac fermions…
A well-known open problem in general relativity, dating back to 1972, has been to prove Price's law for an appropriate model of gravitational collapse. This law postulates inverse-power decay rates for the gravitational radiation flux on…
We derive the large time asymptotics of initially regular and localized solutions of the Teukolsky equation on the exterior of a subextremal Kerr black hole for any half integer spin. More precisely, we obtain the leading order term…
We investigate dispersive estimates for the massless three dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies a $\langle t\rangle^{-1}$ decay rate as an operator from $L^1$ to $L^\infty$…
The interior of Schwarzschild black hole is quantized by the method of loop quantum gravity. The Hamiltonian constraint is solved and the physical Hilbert space is obtained in the model. The properties of a Dirac observable corresponding to…
We compute the spectrum of normalizable fermion bound states in a Schwarzschild black hole background. The eigenstates have complex energies. The real part of the energies, for small couplings, closely follow a hydrogen-like spectrum. The…
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 prove a sharp-in-time dispersive estimate of the Dirac equation on spinor bundles over the real hyperbolic space. Compared with the Euclidean counterparts, our result shows that the dispersive estimate differs between short and long…
To find what influence the charge of the black hole $Q$ will bring to the evolution of the quasinormal modes, we calculate the quasinormal frequencies of the neutrino field (charge $e=0$) perturbations and those of the massless Dirac field…
We prove that the Schwarzschild black hole is linearly stable under electromagnetic and gravitational perturbations. Our method is to show that for spin $s=1$ or $s=2$, solutions of the Teukolsky equation with smooth, compactly supported…
We report on a numerical study of the spherically symmetric collapse of a self-gravitating massless scalar field. Earlier results of Choptuik(1992, 1994) are confirmed. The field either disperses to infinity or collapses to a black hole,…
The late-time tail behaviors of massive scalar fields are examined analytically in the background of a black hole with a global monopole. It is found that the presence of a solid deficit angle in the background metric makes the massive…
In this paper, we study the propagations of external fields in Horndeski theory, including the scalar field, electromagnetic field and Dirac field. We extensively explore the quasinormal frequencies, time evolution, greybody factors and…
We discuss whether the minimally coupled massless Klein-Gordon and Dirac fields have well defined quasinormal modes in single horizon, asymptotically flat two-dimensional black holes. To get the result we solve the equations of motion in…
We determine the largest non-trivial rate of exponential decay at infinity for solutions to the Dirac equation \begin{equation*} \mathcal{D}_n \psi + \mathbb{V} \psi = 0 \quad \text{ in }\mathbb{R}^n, \end{equation*} being $\mathcal{D}_n$…
We compute the quasinormal modes of massive scalar and Dirac fields within the framework of asymptotically de Sitter black holes in Euler-Heisenberg non-linear electrodynamics. We pay particular attention to the regime $\mu M/m_{P}^2 \gg…
We study the wave equation on the real line with a potential that falls off like $|x|^{-\alpha}$ for $|x| \to \infty$ where $2 < \alpha \leq 4$. We prove that the solution decays pointwise like $t^{-\alpha}$ as $t \to \infty$ provided that…
We study massless scalar, electromagnetic, and Dirac perturbations of the exact asymptotically flat regular black hole supported by a phantom Dirac--Born--Infeld scalar. Using the Pad\'e-improved WKB method, with a time-domain Prony check…