Sharp decay estimates for massless Dirac fields on a Schwarzschild background

Peeling of Dirac and Maxwell Fields on a Schwarzschild background

Dirac-sobolev Inequalities and Estimates for the Zero Modes of Massless Dirac Operators

The paper analyses the decay of any zero modes that might exist for a massless Dirac operator H := α·(1/i)∇+Q, where Q is 4 × 4-matrix-valued and of order O(|x|−1) at infinity. The approach is based on inversion with respect to the unit sphere in R and establishing embedding theorems for Dirac-Sobolev spaces of spinors f which are such that f and Hf lie in ( L(R) )4 , 1 ≤ p < ∞.

Asymptotic tails of massive scalar fields in Schwarzschild background

We investigate the asymptotic tail behavior of massive scalar fields in Schwarzschild background. It is shown that the oscillatory tail of the scalar field has the decay rate of t−5/6 at asymptotically late times, and the oscillation with the period 2π/m for the field mass m is modulated by the long-term phase shift. These behaviors are qualitatively similar to those found in nearly extreme Rei...

Radiation Fields on Schwarzschild Spacetime

In this paper we define the radiation field for the wave equation on the Schwarzschild black hole spacetime. In this context it has two components: the rescaled restriction of the time derivative of a solution to null infinity and to the event horizon. In the process, we establish some regularity properties of solutions of the wave equation on the spacetime. In particular, we prove that the reg...

Sharp error estimates for a discretisation of the 1D convection/diffusion equation with Dirac initial data

This paper derives sharp l∞ and l1 estimates of the error arising from an explicit approximation of the constant coefficient 1D convection/diffusion equation with Dirac initial data. The analysis embeds the discrete equations within a semi-discrete system of equations which can be solved by Fourier analysis. The error estimates are then obtained though asymptotic approximation of the integrals ...