Radially falling test particle approaching an evaporating black hole

A simple model for an evaporating non-rotating black hole is considered, employing a global time that does not become singular at the putative horizon. The dynamics of a test particle falling radially towards the center of the black hole is then investigated. Contrary to a previous approach, we find that the particle may pass the Schwarzschild radius before the black hole has gone. Backreaction effects of Hawking radiation on the space-time metric are not considered, rather a purely kinematical point of view is taken here. The importance of choosing an appropriate time coordinate when describing physical processes in the vicinity of the Schwarzschild radius is emphasized. For a shrinking black hole, the true event horizon is found to be inside the sphere delimited by that radius.Comment: 12 pages, 3 figures, revised version, likely to be accepted by Canadian Journal of Physic

Why the Bradley aberration cannot be used to measure absolute speeds. A comment

In a recent article in this journal [G. Sardin, Measure of the absolute speed through the Bradley aberration of light beams on a three-axis frame, Europhys. Lett. 53 (2001) 310], Sardin proposed to use the Bradley aberration of light for the construction of a speedometer capable of measuring absolute speeds. The purpose of this comment is to show that the device would not work.Comment: 2 pages, LaTeX, accepted for Europhysics Letter

Amplitude equations for systems with long-range interactions

We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by integral transforms. We arrive at the interface equation via long-wave asymptotics. As an example, we treat the Grinfeld instability, and we also give a result for the Saffman-Taylor instability. It turns out that the long-range interaction survives the long-wave limit and shows up in the final equation as a nonlocal and nonlinear term, a feature that to our knowledge is not shared by any other known long-wave equation. The form of this particular equation will then allow us to draw conclusions regarding the universal dynamics of systems in which nonlocal effects persist at the level of the amplitude description.Comment: LaTeX source, 12 pages, 4 figures, accepted for Physical Review

Large amplitude behavior of the Grinfeld instability: a variational approach

In previous work, we have performed amplitude expansions of the continuum equations for the Grinfeld instability and carried them to high orders. Nevertheless, the approach turned out to be restricted to relatively small amplitudes. In this article, we use a variational approach in terms of multi-cycloid curves instead. Besides its higher precision at given order, the method has the advantages of giving a transparent physical meaning to the appearance of cusp singularities and of not being restricted to interfaces representable as single-valued functions. Using a single cycloid as ansatz function, the entire calculation can be performed analytically, which gives a good qualitative overview of the system. Taking into account several but few cycloid modes, we obtain remarkably good quantitative agreement with previous numerical calculations. With a few more modes taken into consideration, we improve on the accuracy of those calculations. Our approach extends them to situations involving gravity effects. Results on the shape of steady-state solutions are presented at both large stresses and amplitudes. In addition, their stability is investigated.Comment: subm. to EPJ