70,592 research outputs found
Particle production from marginally trapped surfaces of general spacetimes
We provide a general formalism that allows to analyze the phenomenon of
tunneling in arbitrary spacetimes. We show that a flux of particles produced by
tunneling through general marginally trapped surfaces may be perceived by some
privileged observers. We discuss how this particle perception can be related to
Hawking/Unruh radiation in specific cases. Our approach naturally leads to an
expression for the effective surface gravity of marginally trapped surfaces.
The procedure is applicable to general astrophysical and cosmological dynamical
situations. Some practical examples for known and new cases are provided.Comment: 24 pages, 2 figures. Section 4.2, concerning the analysis of the
Kerr-Vaidya solution, has been rewritten, correcting mistakes in previous
versions. The corrected calculations do support our claims. A corrigendum has
also been sent to CQG. New references added. Some of the mistakes in previous
versions are actually common and spread in the literature on the Kerr-Vaidya
solutio
Weak Conservation Laws for Minimizers which are not Pontryagin Extremals
We prove a Noether-type symmetry theorem for invariant optimal control
problems with unrestricted controls. The result establishes weak conservation
laws along all the minimizers of the problems, including those minimizers which
do not satisfy the Pontryagin Maximum Principle.Comment: Accepted for presentation (Paper No: 113) at the 2nd International
Conference "Physics and Control" (PhysCon 2005), August 24-26, 2005, Saint
Petersburg, Russia. To appear in the respective Conference Proceeding
Lipschitzian Regularity of the Minimizing Trajectories for Nonlinear Optimal Control Problems
We consider the Lagrange problem of optimal control with unrestricted
controls and address the question: under what conditions we can assure optimal
controls are bounded? This question is related to the one of Lipschitzian
regularity of optimal trajectories, and the answer to it is crucial for closing
the gap between the conditions arising in the existence theory and necessary
optimality conditions. Rewriting the Lagrange problem in a parametric form, we
obtain a relation between the applicability conditions of the Pontryagin
maximum principle to the later problem and the Lipschitzian regularity
conditions for the original problem. Under the standard hypotheses of
coercivity of the existence theory, the conditions imply that the optimal
controls are essentially bounded, assuring the applicability of the classical
necessary optimality conditions like the Pontryagin maximum principle. The
result extends previous Lipschitzian regularity results to cover optimal
control problems with general nonlinear dynamics.Comment: This research was partially presented, as an oral communication, at
the international conference EQUADIFF 10, Prague, August 27-31, 2001.
Accepted for publication in the journal Mathematics of Control, Signals, and
Systems (MCSS). See http://www.mat.ua.pt/delfim for other work
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