On an Exact Cylindrically Symmetric Solution in a Born-Infeld Type Theory of Gravity

In this work, we derive an exact vacuum solution for a cylindrically symmetric metric in an extended gravity theory developed by Novello, De Lorenci and Luciane (hereafter referred to as the NDL theory) which is inspired in the Born-Infeld theory. The main goal of this paper is to nd a cosmic string solution for the NDL theory. However, a careful analysis of the metric shows that it is asymptotically singular and therefore does not represent a cosmic string solution.