61 research outputs found
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
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
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
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