Gravitino perturbations in Schwarzschild black holes

TL;DR

This paper studies the evolution of massless gravitino perturbations in Schwarzschild black holes, identifying quasinormal modes and how the black hole's response varies with the spin of the perturbing field.

Contribution

It provides the first detailed analysis of gravitino perturbations in Schwarzschild black holes, improving frequency calculations with higher-order WKB methods and comparing them with Prony fitting results.

Findings

Quasinormal frequencies are accurately determined using sixth order WKB and Prony methods.

Black hole response varies with perturbing field spin, affecting the quality factor.

The evolution of gravitino perturbations follows the typical three-stage pattern seen in other fields.

Abstract

We consider the time evolution of massless gravitino perturbations in Schwarzschild black holes, and show that as in the case of fields of other values of spin, the evolution comes in three stages, after an initial outburst as a first stage, we observe the damped oscillations characteristic of the quasinormal ringing stage, followed by long time tails. Using the sixth order WKB method and Prony fitting of time domain data we determine the quasinormal frequencies. There is a good correspondence between the results obtained by the above two methods, and we obtain a considerable improvement with respect to the previously obtained third order WKB results. We also show that the response of a black hole depends crucially on the spin class of the perturbing field: the quality factor becomes a decreasing function of the spin for boson perturbations, whereas the opposite situation appears for fermion ones.