Spin- 3/2 fields in D -dimensional Schwarzschild black hole spacetimes

In previous works we have studied spin-3/2 fields near four-dimensional Schwarzschild black holes. The techniques we developed in that case have now been extended here to show that it is possible to determine the potential of spin-3/2 fields near D-dimensional black holes by exploiting the radial symmetry of the system. This removes the need to use the Newman-Penrose formalism, which is difficult to extend to D-dimensional spacetimes. In this paper we will derive a general D-dimensional gauge-invariant effective potential for spin-3/2 fields near black hole systems. We then use this potential to determine the quasinormal modes and absorption probabilities of spin-3/2 fields near a D-dimensional Schwarzschild black hole.