Scalar field scattering by a Lifshitz black hole under a non-minimal coupling

TL;DR

This paper analyzes scalar field scattering in a Lifshitz black hole background with non-minimal coupling, deriving analytical solutions, quasinormal modes, and studying stability, reflection, absorption, and cross sections.

Contribution

It provides the first analytical solutions for scalar fields with non-minimal coupling in Lifshitz black holes, including quasinormal modes and stability analysis.

Findings

Quasinormal modes are stable under certain conditions.

Absorption cross section is significantly affected by non-minimal coupling.

Analytical solutions are obtained for scalar fields in this background.

Abstract

We study the behavior of a scalar field under a z = 3 Lifshitz black hole background, in a way that is non-minimally coupled to the gravitational field. A general analytical solution is obtained along with two sets of quasinormal modes associated to different boundary conditions that can be imposed on the scalar field, non-minimal coupling parameter appears explicitly on these solutions. Stability of quasinormal modes can be studied and ensured for both cases. Also, the reflection and absorption coefficients are calculated, as well as the absorption cross section which features an interesting behavior because of being attenuated by terms strongly dependant on the non-minimal coupling. By a suitable change of variables a soliton solution can also be obtained and the stability of the quasinormal modes are studied and ensured.