Spin-3/2fields inD-dimensional Schwarzschild black hole spacetimes

Abstract

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.

Quasi normal modes for a spin-3/2 field in a 4-dimensional Reissner-Nordström black hole background.

“…The case of Q = M represents the extremal case for our black hole, which we will investigate and compare these results to those obtained for the Schwarzschild black hole given in Ref. [6]. We hope that by considering the extremal case we will identify any significant differences in our new results.…”

“…In the above expressionsφ 1 andφ 2 are the wave functions associated to our fields, andλ are the eigenvalues for our spinors on a sphere given asλ = j + 1/2 with j = 3/2, 5/2, ... [6].…”

Semi-Analytic Techniques for Solving Quasi-Normal Modes

“…With recent progress in spin-3/2 fields [11], we find that these results greatly overlap with some of the spin-3/2 particles, which are represented by the relations in the radial equations of the transverse and traceless eigenmodes. In this section, as an example, we are going to show how to reproduce the results by the AIM.…”

“…For the case of bosonic fields, an earlier study by Rubin and Ordóñez presented a systematic study [7,8] as well as in a later work by Higuchi [9]. For the case of fermionic fields, Camporesi and Higuchi presented the eigenmodes for spinor fields on arbitrary dimensional spheres [10], and in a recent work by the authors [11], the spinor-vector eigenmodes on arbitrary dimensional spheres were derived using a similar approach to Camporesi and Higuchi's methods. In this section, we review the structure of these eigenmodes, especially for the case of spinor-vector fields, which shall be presented with the characteristics of both spinor and vector fields.…”

“…In this section, we are going to present a discussion of our recent work [11] on the spin-3/2 fields in general dimensional Schwarzschild spacetimes. Note that, this section will not go into as great a detail as the previous one but shall just list some improvements made in light of recent considerations.…”