358 research outputs found
Maine De Biran. (i 766-1 824.) One of the Founders of Modern Psychology. With Portrait of Victor Cousin (1792-1867).
Pierre Bayle. (1647-1706). Scholar and Theological Critic. The Precursor of the Religious Philosophy of the Eighteenth Century.
Modern French Philosophy. The Ideologists and Traditionalists. With Half-tone Portraits of Pierre Jean Georges Cabanis (1757-1808) and Joseph De Maistre (1754-1821).
Black hole lasers, a mode analysis
We show that the black hole laser effect discovered by Corley & Jacobson
should be described in terms of frequency eigenmodes that are spatially bound.
The spectrum contains a discrete and finite set of complex frequency modes
which appear in pairs and which encode the laser effect. In addition, it
contains real frequency modes that form a continuous set when space is
infinite, and which are only elastically scattered, i.e., not subject to any
Bogoliubov transformation. The quantization is straightforward, but the
calculation of the asymptotic fluxes is rather involved. When the number of
complex frequency modes is small, our expressions differ from those given
earlier. In particular, when the region between the horizons shrinks, there is
a minimal distance under which no complex frequency mode exists, and no
radiation is emitted. Finally, we relate this effect to other dynamical
instabilities found for rotating black holes and in electric fields, and we
give the conditions to get this type of instability.Comment: 19 pages, 3 figures, main changes: new figure and new Sec.6
`conditions for having a laser effect', final version accepted in PR
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