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