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This paper has been withdrawn by the author. The paper has been accepted for publication in Communications on Pure and Applied Mathematics.
This paper has been withdrawn due to a crucial theoretical error.
This paper has been withdrawn by the author due to errors and bad formalization.
This paper has been withdrawn by the authors
This paper has been withdrawn by the authors. This is due to the fact that it has been substantially revised. As a consequence title and aim of the contents
In this paper, we propose a Cauchy type problem to the timelike Lorentzian eikonal equation on a globally hyperbolic space-time. For this equation, as the value of the solution on a Cauchy surface is known, we prove the existence of…
This paper has been withdrawn by the authors due to some errors.
They are possible other cases at first done not contemplate. This paper has been withdrawn by the author due to a crucial sign error in equation 1 page 4
This paper has been withdrawn due to crucial errors.
The paper has been withdrawn
This paper has been withdrawn by the author(s), due a crucial i-number error in Eqn. 18.
This paper is withdrawn since there is a problem in the previous paper on which it is based.
This paper has been withdrawn by the authors due to an unlikely results.
This paper is being withdrawn by the authors in order to correct some errors and also to introduce improved theoretical techniques.
This paper has been withdrawn by the author due to a crucial error.
This paper was withdrawn by the author. It turns out that similar ideas have been presented before. The author apologizes.
This paper has been withdrawn by the authors, due a crucial error.
This paper has been withdrawn by the author due to new results to be added.
Withdrawn by author. This paper was mistakenly submitted twice (See nucl-th/0604008)
This paper was withdrawn by the authors due to significant new findings. A new paper on the same topic has been submitted as physics/0310159.