Relating black holes in two and three dimensions

Abstract

The three dimensional black hole solutions of Ba\~nados, Teitelboim and Zanelli (BTZ) are dimensionally reduced in various different ways. Solutions are obtained to the Jackiw-Teitelboim theory of two dimensional gravity for spinless BTZ black holes, and to a simple extension with a non-zero dilaton potential for black holes of fixed spin. Similar reductions are given for charged black holes. The resulting two dimensional solutions are themselves black holes, and are appropriate for investigating exact ``S-wave'' scattering in the BTZ metrics. Using a different dimensional reduction to the string inspired model of two dimensional gravity, the BTZ solutions are related to the familiar two dimensional black hole and the linear dilaton vacuum.Comment: 12 pages, CTP #2181, January 199

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

“…1 Taking into account the known advantages of the two-dimensional gravity models in the analysis of many physical phenomena [47,48], it is unexpected that for two-dimensional black holes their QNF have not been studied in more detail. Motivated by this fact here we extend the previous results and calculate the QNF of the uncharged Achucarro-Ortiz 2 (UAO) black hole and of the charged Achucarro-Ortiz (CAO) black hole [49]. In contrast to the black holes studied in Refs.…”

“…Surprisingly, the radial differential equation for the two-dimensional CAO black hole is more complicated than the radial equation of the three-dimensional rotating BTZ black hole. We believe that this result is due (at least in part) to the fact that the spinning BTZ black hole is a constant curvature spacetime [54]- [56], whereas the scalar curvature of the CAO black hole is equal to [49] …”

“…Among the two-dimensional black holes, the UAO black hole is frequently studied [47,48,49]. The metric and dilaton of this black hole are…”

“…Note that if we take l = 1 and hence r 2 + = M , the metrics (1) and (3) are equal. We can get this two-dimensional spacetime from the three-dimensional static BTZ black hole [54]- [56] by means of a dimensional reduction procedure, in such a way that the UAO black hole is a solution to the equations of motion derived from the action [49] …”

“…A generalization of the two-dimensional UAO black hole is the CAO black hole whose line element is [49] …”