Fermion perturbations in string-theory black holes II: the higher dimensional case

TL;DR

This paper investigates the evolution of massless fermion fields in higher-dimensional string-theory black holes, determining quasinormal modes, late-time decay, and their dependence on black hole charges and spacetime dimensions.

Contribution

It provides a comprehensive analysis of fermion perturbations in higher-dimensional stringy black holes, including numerical and analytical calculations of quasinormal frequencies and decay rates.

Findings

Quasinormal frequencies match between numerical and WKB methods.

Late-time decay exponents depend on spacetime dimensionality.

Frequencies and damping are influenced by black hole charges.

Abstract

In this paper we report the results of a detailed investigation of the complete time evolution of massless fermion fields propagating in spacetimes of higher dimensional stringy black hole solutions, obtained from intersecting branes in string/$M$ theory. We write the Dirac equation in $D$-dimensional spacetime in a form suitable to perform a numerical integration of it, and using a Prony fitting of the time domain data, we determine the quasinormal frequencies that characterize the test field evolution at intermediary times. We also present the results obtained for the quasinormal frequencies using a sixth order WKB approximation, that are in perfect agreement with the numerical results. The power law exponents that describe the field relaxation at very late times are also determined, and we show that they depends upon the dimensionality of space-time, and are identical to that associated with the relaxation of boson fields for odd dimensions. The dependance of the frequencies and damping factor of the spinor field with the charges of the stringy black hole are studied.