New modes for massive Dirac field in higher dimensional Black Holes

In this letter we derive new modes for massive Dirac field in the background of a higher-dimensional Schwarzschild black hole. We use in our approach the Cartesian gauge defined in local frames. We work in the context of ADD-like theories, assuming that the Standard Model fields (fermions and bosons) live only on a (3+1)-dimensional brane and the extra dimensions of space can be large in size.