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

Abstract

We calculate exactly the quasinormal frequencies of Klein-Gordon and Dirac test fields propagating in two-dimensional uncharged Achucarro-Ortiz black hole. For both test fields we study whether the quasinormal frequencies are well defined in the massless limit. We use their values to discuss the classical stability of the quasinormal modes in uncharged Achucarro-Ortiz black hole and to check the recently proposed Time Times Temperature bound. Furthermore we extend some of these results to the charged Achucarro-Ortiz black hole.

Entropy Spectra of Single Horizon Black Holes in Two Dimensions

“…For the AQNF of single horizon black holes it is common to find the behavior [19]- [23], [26,60,61]: (i) Their real parts go to a constant; (ii) Their imaginary parts behave as |ω I,n | ≈ nκq. For example, for the AQNF of the gravitational perturbations moving in the four-dimensional Schwarzschild black hole [16], [19]- [23] we obtain that ω R,n = ln(3)/8πM and ω I,n = nκq with q = 1 (see the formula (3)).…”

“…Our main reason is that for these two black holes the parameter b is outside the interval 0 < b < 1, because for a conformally related spacetime to the Witten black hole the parameter b is equal to zero, whereas for the AdS 2 black hole we find that b = −1 [27]. Furthermore for these two black holes their QNF are known in exact form [57]- [61].…”

“…For the AdS 2 black hole the QNF of the massive Klein-Gordon and Dirac fields are calculated exactly in Ref. [61]. For the Klein-Gordon field its QNF are…”

Quasinormal modes and hidden conformal symmetry in the Reissner–Nordström black hole

“…(69) can be transformed into a standard hypergeometric equation [21] x(1 − x)y ′′ + [c − (a + b + 1)x]y ′ − aby = 0 (71)…”

Quasinormal Frequencies of a Two-Dimensional Asymptotically Anti-de Sitter Black Hole of the Dilaton Gravity Theory

“…Furthermore, in 2D spacetimes the equations of motion for classical fields simplify and we can study in more detail several physical phenomena, for example, the way in which a 2D black hole reacts when it is perturbed. The QNFs of 2D spacetimes have been studied in recent times (Li et al, 2001;Kettner et al, 2004;Becar et al, 2007;Zelnikov, 2008;López-ortega, 2009;Becar et al, 2010;López-ortega, 2011;López-Ortega and Vega-Acevedo, 2011;Cordero et al, 2012;Myung and Moon, 2012;Estrada-Jiménez et al, 2013;Stetsko, 2017;Jusufi et al, 2018;Sakallı et al, 2018;Mirbabayi, 2020;Bhattacharjee et al, 2021;Kanzi and Sakallı, 2021;Sakalli and Tokgöz Hyusein, 2021). Exact results for the QNFs have previously found (Li et al, 2001;Kettner et al, 2004;Becar et al, 2007;Zelnikov, 2008;López-ortega, 2009;Becar et al, 2010;López-ortega, 2011;López-Ortega and Vega-Acevedo, 2011;Cordero et al, 2012;Myung and Moon, 2012;Estrada-Jiménez et al, 2013;Stetsko, 2017;Jusufi et al, 2018;Sakallı et al, 2018;Mirbabayi, 2020;Bhattacharjee et al, 2021;Kanzi and Sakallı, 2021;Sakalli and Tokgöz Hyusein, 2021), but for some asymptotically adS 2D backgrounds a numerical calculation is necessary (Corder...…”