Kerr-Schild Method and the Geodesic Structure in a Codimension-2 Brane Black Holes

In this work we consider black hole solutions in a five-dimensional gravity. We include a Gauss-Bonnet term in the bulk and an induced gravity term on a 2-brane of codimension-2. Applying the Kerr-Schild method\footnote{A. H. Taub, Ann. of Phys. \textbf{220}, 326 (1981).} to a background known solution\footnote{B. Cuadros--Melgar, E. Papatonopoulos, M. Tsoukalas and V. Zamarias, \textit{Phys. Rev. Lett.} \textbf{100, }221601 (2008).} we have been able to generate additional solutions which include charge, angular momentum and a scalar field. In an effort to understand the geometric structure of these new spacetimes, we display a set of relevant geodesic families generated in these geometries.