Scalar perturbations of two-dimensional Horava–Lifshitz black holes

Abstract

In this article, we study the stability of black hole solutions found in the context of dilatonic Horava-Lifshitz gravity in 1 + 1 dimensions by means of the quasinormal modes approach. In order to find the corresponding quasinormal modes, we consider the perturbations of massive and massless scalar fields minimally coupled to gravity. In both cases, we found that the quasinormal modes have a discrete spectrum and are completely imaginary, which leads to damping modes. For a massive scalar field and a nonvanishing cosmological constant, our results suggest unstable behavior for large values of the scalar field mass.

Fermionic quasinormal modes for two-dimensional Hořava–Lifshitz black holes

“…[36]. Comparing the obtained result for quasinormal frequencies with the corresponding result for the scalar perturbation, we conclude that the fermion field perturbation is stable for arbitrary mass of the fermion field whereas for the scalar field perturbations it might be unstable for sufficiently large masses of the field [34]. It can also be shown that the imposed boundary conditions at infinity lead to the vanishing flux, defined by Eq.…”

“…The solution which fulfills the imposed boundary condition has a purely imaginary discrete spectrum. It should be noted that the fermion field of arbitrary mass is stable in that geometry and as we mentioned before, for scalar field perturbations it might be unstable for large masses of the field [34].…”

“…The latter metric can be rewritten in a bit different form after some kind of transformation of coordinates [34]:…”

“…It should be remarked that the quasinormal modes for scalar perturbations in the same black hole background were considered in Ref. [34].…”

“…(33) namely the function K n (z) can be introduced as limit of the function K ν (z) when ν → n. The behaviour of the solution K n (z) at infinity and at the horizon is similar to the case of noninteger ν and it means that it also satisfies the above mentioned conditions for the quasinormal modes, but there is no specific requirement that might distinguish integer values of the parameter ν from noninteger ones. In the case of scalar particles the behaviour of the particle flux at infinity was also analyzed [34]. Taking into account the definition of the flux for the Dirac particles we can write…”