Split fermion quasinormal modes

Abstract

In this paper we use the conformal properties of the spinor field to show how we can obtain the fermion quasi-normal modes for a higher dimensional Schwarzschild black hole. These modes are of interest in so called split fermion models, where quarks and leptons are required to exist on different branes in order to keep the proton stable. As has been previously shown, for brane localized fields, the larger the number of dimensions the faster the black hole damping rate. Moreover, we also present the analytic forms of the quasi-normal frequencies in both the large angular momentum and the large mode number limits.

Semi-Analytic Techniques for Solving Quasi-Normal Modes

“…The results using the thirdorder WKB methods are the same as presented in our previous work [13], where for completeness we also list the sixth-order WKB results. Table 3.…”

“…The QNMs for Dirac particles in the higher dimensional Schwarzschild black hole spacetimes had been done in the earlier work by some of the authors [13] using the third-order WKB approximation but not the AIM. 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.…”

“…For the fermionic fields in the four-dimensional Schwarzschild case, the effective potential can be shown as follows [13,14]:…”

Quasinormal modes for doubly rotating black holes

“…As was shown in [40] different choices of this point can worsen or improve the speed of the convergence. In the absence of a clear selection criterion we simply choose this point conveniently in the middle of the domains: methods.…”

“…As we shall see, for D ≥ 6, in the limit of keeping only two rotation parameters a total of two Jacobi coordinates survive. The D = 5 case will be considered in a separate work [30].…”