Dirac Fermions in Non-trivial Topology Black Hole Backgrounds

TL;DR

This paper investigates the behavior of Dirac fermions in various non-trivial black hole backgrounds, revealing how topology influences fermionic decay rates and eigenvalues, with implications for black hole physics and quantum fields.

Contribution

It provides analytical insights into the intermediate and late-time behavior of Dirac fermions in black holes with non-trivial topologies, highlighting the effects of global monopoles and cosmic strings.

Findings

Late-time decay rate is proportional to t^{-5/6}.

Behavior depends on topology, mass, and mode number.

Topology modifies eigenvalues of the Dirac operator.

Abstract

We discuss the behaviour of the Dirac fermions in a general spherically symmetric black hole background with a non-trivial topology of the event horizon. Both massive and massless cases are taken into account. The analytical studies of intermediate and late-time behaviour of massive Dirac hair in the background of a black hole with a global monopole and dilaton black hole pierced by a cosmic string will be conducted. It was revealed that in the case of a global monopole swallowed by a static black hole the intermediate late-time behaviour depends on the mass of the Dirac field, the multiple number of the wave mode and the global monopole parameter. The late-time behaviour is quite independent of these factors and has the decay rate proportional to $t^{-5/6}$. As far as the black hole pierced by a cosmic string is concerned the intermediate late-time behaviour depends only on the hair mass and the multipole number of the wave mode while the late-time behaviour dependence is the same as in the previous case. The main modification stems from the topology of the $S^2$ sphere pierced by a cosmic string. This factor modifies the eigenvalues of the Dirac operator acting on the transverse manifold.