Semi-analytical and numerical solutions to Teukolsky equations for large fermion mass over black hole mass ratio

Abstract

In a recent paper, we have studied the Teukolsky equations for fermions with mass $m_e\neq 0$ and rotating black hole of mass $M$. There, we have studied two cases: $\tilde{m}_e=m_e\,M^{-1}\ll 1$ and $a\omega\ll 1$; $\tilde{m}_e\ll 1$ and $a\omega \gtrsim 1$. Here we study the two remaining case case in which $\tilde{m}_e\gtrsim 1$ and $a\omega\ll 1$ using a semi-analytical approach and $\tilde{m}_e\gtrsim 1$ and $a\omega\gtrsim 1$ using a numerical approach. This case could be of some interest for the study of the interactions of fermions with small black holes, such as those formed in the last stages of the the Hawking evaporation process.