Axisymmetric Dirac-Nambu-Goto branes on Myers-Perry black hole backgrounds

Stationary, D-dimensional test branes, interacting with N-dimensional Myers-Perry bulk black holes, are investigated in arbitrary brane and bulk dimensions. The branes are asymptotically flat and axisymmetric around the rotation axis of the black hole with a single angular momentum. They are also spherically symmetric in all other dimensions allowing a total of O(1)xO(D-2) group of symmetry. It is shown that even though this setup is the most natural extension of the spherical symmetric problem to the simplest rotating case in higher dimensions, the obtained solutions are not compatible with the spherical solutions in the sense that the latter ones are not recovered in the non-rotating limit. The brane configurations are qualitatively different from the spherical problem, except in the special case of a 3-dimensional brane. Furthermore, a quasi-static phase transition between the topologically different solutions cannot be studied here, due to the lack of a general, stationary, equatorial solution.