Euclidean Dilaton Black Hole Vortex and Dirac Fermions

TL;DR

This paper investigates how Dirac fermion modes behave around Euclidean dilaton black holes with Abelian Higgs vortices, revealing conditions under which fermion fields can act as superconducting hair on black holes.

Contribution

It introduces a detailed analysis of Dirac fermion modes in dilaton black hole backgrounds with vortices, showing their potential to form superconducting hair.

Findings

Fermion modes depend on cosmic string winding number and black hole surface gravity.

Nontrivial fermion configurations can be supported as superconducting hair.

Localization of fermion modes varies with black hole and vortex parameters.

Abstract

We considered the behaviour of Dirac fermion modes in the background of Euclidean dilaton black hole with an Abelian Higgs vortex passing through it. Fermions were coupled to the fields due to the superconducting string model. The case of nonextremal and extremal charged black hole in the theory with arbitrary coupling constant between dilaton field and U(1)-gauge field were considered. We elaborated the cases of zero and non-zero Dirac fermion modes. One finds the evidence that the system under consideration can support fermion fields acting like superconducting hair on black hole in the sence that nontrivial spinor field configuration can be carried by Euclidean spherically symmetric charged dilaton black hole. It was revealed that the localization of Dirac fermion modes depended on the cosmic string winding number and the value of black hole surface gravity.