Asymptotic structure of the Einstein-Maxwell theory on AdS3

Abstract

The asymptotic structure of AdS spacetimes in the context of General Relativity coupled to the Maxwell field in three spacetime dimensions is analyzed. Although the fall-off of the fields is relaxed with respect to that of Brown and Henneaux, the variation of the canonical generators associated to the asymptotic Killing vectors can be shown to be finite once required to span the Lie derivative of the fields. The corresponding surface integrals then acquire explicit contributions from the electromagnetic field, and become well-defined provided they fulfill suitable integrability conditions, implying that the leading terms of the asymptotic form of the electromagnetic field are functionally related. Consequently, for a generic choice of boundary conditions, the asymptotic symmetries are broken down to R ⊗ U (1) ⊗ U (1). Nonetheless, requiring compatibility of the boundary conditions with one of the asymptotic Virasoro symmetries, singles out the set to be characterized by an arbitrary function of a single variable, whose precise form depends on the choice of the chiral copy. Remarkably, requiring the asymptotic symmetries to contain the full conformal group selects a very special set of boundary conditions that is labeled by a unique constant parameter, so that the algebra of the canonical generators is given by the direct sum of two copies of the Virasoro algebra with the standard central extension and U (1). This special set of boundary conditions makes the energy spectrum of electrically charged rotating black holes to be well-behaved.

Einstein-Katz action, variational principle, Noether charges and the thermodynamics of AdS-black holes

“…When D = 0 that extends the results obtained in ref [8]. The expression (4.4) for the mass of asymptotically AdS hairy black holes is the second result of this paper.…”

“…One may therefore argue that D must be taken to be zero, in which case the scalar field asymptotic behaviour preserves the AdS symmetry, see e.g. [3] or [8].…”

“…Using (3.5) and (3.6) one haŝ 8) JHEP08 (2016)049 and, using (3.10) and (3.11) as well as the metrics (3.6) and (3.8):…”

Surface charges toolkit for gravity

“…The charges formulas for the standard asymptotia blow up when is computed for this black hole. In [49,50] the asymptotic analysis has been widened to work out the asymptotic charges correctly. Here, we take a different perspective and use the surface charge formula corresponding to the full theory.…”

Charged dilatonic black holes in gravity’s rainbow

“…This phase transition was reconsidered through the use of the AdS/CFT correspondence by Witten [80]. This work motivated a great deal of research to be conducted in context of black holes thermodynamics, stability, and their phase transitions [81][82][83][84][85][86][87][88][89][90].…”