In previous works we have studied spin-3/2 fields near 4-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 space-times. In this paper we will derive a general Ddimensional gauge invariant effective potential for spin-3/2 fields near black hole systems. We then use this potential to determine the quasi-normal modes and absorption probabilities of spin-3/2 fields near a D-dimensional Schwarzschild black hole.

In this paper we consider spin-3/2 fields in a D-dimensional Reissner-Nordström black hole spacetime. As these spacetimes are not Ricci-flat, it is necessary to modify the covariant derivative to the supercovariant derivative, by including terms related to the background electromagnetic fields, so as to maintain the gauge symmetry. Using this supercovariant derivative we arrive at the corresponding Rarita-Schwinger equation in a charged black hole background. As in our previous works, we exploit the spherically symmetry of the spacetime and use the eigenspinor-vectors on an N -sphere to derive the radial equations for both non-transverse-traceless (non-TT) modes and TT modes. We then determine the quasi-normal mode and absorption probabilities of the associated gauge-invariant variables using the WKB approximation and the asymptotic iteration method. We then concentrate on how these quantities change with the charge of the black hole, especially when they reach the extremal limits.whereis antisymmetric product of Dirac gamma matrices, ∇ ν is the covariant derivative, and ψ α is the spin-3/2 field. In four dimensional black hole spacetimes the Rarita-Schwinger equations are usually analyzed in the Newman-Penrose formalism. However, this formalism cannot be extended to higher dimensions in a straightforward way. In our previous works [3,4] we have tried an alternative approach to deal with spherically symmetric black hole cases. Using a complete set of eigenspinor-vectors on N -spheres, we were able to separate the radial and angular parts of the Rarita-Schwinger equation. In this paper we would like to extend our considerations to charged black hole spacetimes.The Rarita-Schwinger equation is invariant under the gauge transformationwhere ϕ is a gauge spinor, provided that the background spacetime is Ricci-flat [3,4]. This is not the case for charged black holes, nor for black holes in de Sitter or anti-de Sitter spaces. To maintain the gauge symmetry in those cases it is necessary to modify the covariant derivative into the so-called the "supercovariant derivative". This is done by adding terms related to the cosmological constant and the electromagnetic field of the black hole. Here we shall concentrate on charged Reissner-Nordström black holes in asymptotically flat spacetimes, where in the following section we shall show in detail how the supercovariant derivative is constructed in this case.Using the supercovariant derivative we are able to obtain the Rarita-Schwinger equation for spin-3/2 fields in Reissner-Nordström black hole spacetimes. Since the spacetime is still spherically symmetric, it is possible, as in our previous works, to derive the radial equations for each component of the spin-3/2 field using eigenspinor-vectors on the Nsphere. However, the component fields are not gauge invariant, while the physical fields