Siklos waves with torsion in 3D

Abstract

Starting from the Siklos waves in general relativity with a cosmological constant, interpreted as gravitational waves on the anti-de Sitter background, a new class of exact torsion waves is constructed in the framework of three-dimensional gravity with propagating torsion. In the asymptotic limit, the geometry of torsion waves takes the antide Sitter form. In the sector with massless torsion modes, we found a set of asymptotic conditions that leads to the conformal asymptotic symmetry.

Vaidya-like exact solutions with torsion

“…The first step in this direction was made by constructing the Bañados-Teitelboim-Zanelli (BTZ) black hole with torsion [9]. Then, we showed that gravitational waves can be naturally incorporated into the PGT dynamical framework [10,11]. The purpose of the present work is to examine a PGT generalization of the Oliva-Tempo-Troncoso (OTT) black hole [12], see also [13], as well as its Vaidya-like extension [14].…”

“…The energy density of this fluid is expressed directly in terms of the metric function B(u), which remains dynamically undetermined. Based on our experience with exact wave solutions in PGT [10,11], we expect that the presence of torsion could lead to a consistent description of the Vaidya-OTT dynamics in vacuum. Further exposition confirms this expectation.…”

“…Following the logic of our approach to exact wave solutions in PGT [10,11], we propose to look for a Vaidya-OTT solution with torsion using the following two assumptions:…”

“…In order to calculate C , one should note that the algebra (5.10) implies δ 0 Γ ≈ Γ + C , where δ 0 Γ is determined by the relations (5.6), and C is identified as the field independent piece on the right-hand side. Then, going over to the Fourier modes L ± n ofG, the algebra (5.10) takes the form of two independent Virasoro algebras, 11) where the classical central charges are equal to each other, c ± = c, with…”

Siklos waves in Poincaré gauge theory

“…In the present work, we focus on a particular class of the gravitational waves, the class of Siklos waves that are vacuum solutions of general relativity with a cosmological constant (GR Λ ), propagating on the AdS background [12]. By generalizing the ideas developed in three dimensions [13], we construct here a class of the four-dimensional Siklos waves with torsion as vacuum solutions of PGT.…”