Quasinormal frequencies of asymptotically flat two-dimensional black holes

Abstract

We discuss whether the minimally coupled massless Klein-Gordon and Dirac fields have well defined quasinormal modes in single horizon, asymptotically flat two-dimensional black holes. To get the result we solve the equations of motion in the massless limit and we also calculate the effective potentials of Schrödinger type equations. Furthermore we calculate exactly the quasinormal frequencies of the Dirac field propagating in the two-dimensional uncharged Witten black hole. We compare our results on its quasinormal frequencies with other already published.

Quasinormal frequencies of asymptotically anti-de Sitter black holes in two dimensions

“…In a similar way to [42], we see that for asymptotically anti-de Sitter two-dimensional black holes the massless Klein-Gordon equation simplifies to a free Schrödinger type equation (see Eqs. (25) and (26) in [42]), and since its solutions do not satisfy the boundary conditions of the QNM, we find that the massless Klein-Gordon field does not have well defined QNF in asymptotically anti-de Sitter two-dimensional black holes.…”

“…Becar et al [39] compute exactly the QNF of the Klein-Gordon field minimally coupled to scalar curvature in the uncharged Witten black hole [43,44] (see also [40]). For this black hole, also Becar et al [41] calculate exactly the QNF of the massless Dirac field and in [42] these results are extended to the massive Dirac field. Furthermore in the last reference it is shown that in asymptotically flat two-dimensional black holes the massless Klein-Gordon and Dirac fields do not have well defined QNM and hence the frequencies calculated in [41] cannot be QNF of the massless Dirac field in the uncharged Witten black hole.…”

“…In Ref. [42] it is shown that the massless Klein-Gordon field does not have well defined QNF in single horizon asymptotically flat two-dimensional black holes. In this reference it is shown that the solutions to the equation of motion do not satisfy the boundary conditions of the QNM for asymptotically flat black holes.…”

“…[38]- [42], [45,46] the UAO and CAO black holes are asymptotically anti-de Sitter. Therefore the boundary condition that the fields satisfy at the asymptotic region is different from the boundary condition imposed in [38]- [42], [45,46]. Although for the two black holes in two dimensions that we study here, their metrics are similar to those of the three-dimensional static and rotating BTZ black holes, in the results for their QNF we find some differences respect to those naively expected.…”

“…[38]- [42]. Zelnikov [38] calculates exactly the QNF of the Klein-Gordon field propagating in a family of two-dimensional black holes.…”