Quasibound states of Schwarzschild acoustic black holes

Abstract

In this paper we study the recently proposed Schwarzschild acoustic black hole spacetime, in which we investigate some physical phenomena related to the effective geometry of this background, including the analogous Hawking radiation and the quasibound states. We calculate the spectrum of quasibound state frequencies and the wave functions on the Schwarzschild acoustic background by using the polynomial condition of the general Heun function and then we discuss the stability of the system. We also compare the resonant frequencies of the Schwarzschild acoustic black hole with the ones by the standard Schwarzschild black hole. Our results may shed some light on the physics of black holes and their analogue models in condensed matter. Moreover, these studies could provide the possibility, in principle, for laboratory testing of effects whose nature is unquestionably associated with purely quantum effects in gravity.

Quasibound states, stability and wave functions of the test fields in 4D Einstein--Gauss--Bonnet gravity

“…In fact, the potentials V + 1 2 and V − 1 2 can be transformed one into another by using the Darboux transformation, which means that the both potentials give the same quasispectrum. Then, we can provide an analytic solution for the radial equation (12) in terms of the general Heun functions [19], by following the approach described in our recent work [20]. It is given by…”

“…In order to derive the characteristic resonance equation, many authors have been using a method that consists of solving the radial equation in two different asymptotic regions and then matching these two radial solutions in their common overlap region. In this paper, we will use the Vieira-Bezerra-Kokkotas method [20,21] to find the resonant frequencies related to quasibound states. This method consists in to obtain the ingoing wave solution at the exterior event horizon and then to impose the polynomial condition related, in this case, to the general Heun functions.…”

“…In this section we will use the Vieira-Bezerra-Kokkotas method [20,21] to derive the wave functions describing massless test particles that propagate in the 4DEGBBH spacetime. This approach consists of using some properties of the general Heun functions, as well as their polynomial (alpha-)condition, to write the general Heun polynomials and then obtains the wave eigenfunctions.…”

“…In our case, general Heun polynomials depend on the spin s, as well as on the angular quantum number l, of the test fields and should be denoted as Hp sln,m (x) and q sln,m . Thus, the general Heun polynomials for the fundamental and first excited modes are given, respectively, by [20] Hp sl0,0 (x) = 1,…”

(In)stability of the charged massive scalar field on the Kerr-Newman spacetime

“…First, to obtain general solutions for the charged massive Klein-Gordon equation in the Kerr-Newman black hole spacetime. Second, to show that the resonant frequencies describing quasibound states may be calculated analytically using the Vieira-Bezerra-Kokkotas method [6,7].…”