Conserved charges in timelike warpedAdS3spaces

Abstract

We consider the timelike version of Warped Anti-de Sitter space (WAdS), which corresponds to the three-dimensional section of the Gödel solution of four-dimensional cosmological Einstein equations. This geometry presents closed timelike curves (CTCs), which are inherited from its four-dimensional embedding. In three dimensions, this type of solutions can be supported without matter provided the graviton acquires mass. Here, among the different ways to consistently give mass to the graviton in three dimensions, we consider the parity-even model known as New Massive Gravity (NMG). In the bulk of timelike WAdS 3 space, we introduce defects that, from the three-dimensional point of view, represent spinning massive particle-like objects. For this type of sources, we investigate the definition of quasi-local gravitational energy as seen from infinity, far beyond the region where the CTCs appear. We also consider the covariant formalism applied to NMG to compute the mass and the angular momentum of spinning particle-like defects, and compare the result with the one obtained by means of the quasi-local stress-tensor. We apply these methods to special limits in which the WAdS 3 solutions coincide with locally AdS 3 and locally AdS 2 × R spaces. Finally, we make some comments about the asymptotic symmetry algebra of asymptotically WAdS 3 spaces in NMG.

Holographic Entanglement Entropy in NMG

“…In order to simplify the discussion, following [39] and setting ℓ = 1, we perform the necessary change of coordinates as…”

Holographic entropy of Warped-AdS3 black holes

“…The mass of Gödel spacetime in NMG has been recently computed in [12], and the result was found to be…”

Supersymmetric solutions of N=(1,1) general massive supergravity

“…In particular, one may look for some stationary, supersymmetric Lifshitz black holes especially since, it is known that they don't exist in N = (1, 1) NMG [18]. It would also be interesting to study thermodynamics and conserved charges [29] of our timelike warped AdS solution (4.23) which has a Killing horizon as shown in appendix B. We were able to give geometric identification of all our solutions except (4.24).…”