Conservation and integrability in lower-dimensional gravity

Abstract

We address the questions of conservation and integrability of the charges in two and three-dimensional gravity theories at infinity. The analysis is performed in a framework that allows us to treat simultaneously asymptotically locally AdS and asymptotically locally flat spacetimes. In two dimensions, we start from a general class of models that includes JT and CGHS dilaton gravity theories, while in three dimensions, we work in Einstein gravity. In both cases, we construct the phase space and renormalize the divergences arising in the symplectic structure through a holographic renormalization procedure. We show that the charge expressions are generically finite, not conserved but can be made integrable by a field-dependent redefinition of the asymptotic symmetry parameters.

Chiral massive news: null boundary symmetries in topologically massive gravity

“…That is the flux is proportional to the Ricci curvature along the null surface. Assuming the classical null curvature condition R ll ≥ 0 the flux is always non-positive, 17 in line with the usual classical intuition that the flux just passes inside (inward) through the null surface. The transformation laws of the integrable parts of the charges are then obtained as,…”

“…There is no propagating degrees of freedom in the VCT sector and hence we are expecting integrable charges. Nonetheless, unlike previous cases [17,24], a choice of slicing is not sufficient to render the charges integrable. It has to be supplemented by an appropriate choice of the Y -ambiguity (2.22).…”

“…It has to be supplemented by an appropriate choice of the Y -ambiguity (2.22). This is similar to the case of asymptotic boundaries where Lee-Wald charges diverge and Y -terms are needed to render finite the charges [17]. In other words, integrability of charges can be used to (partially) fix the Y -ambiguity in the charges.…”

“…We have explored a generic null hypersurface in the 4d Einstein gravity [27], 2d JT gravity and 3d Einstein-Λ [24]. Similar maximal phase space for asymptotic boundaries in 2d and 3d has also been studied [17]. The analysis in [27] was motivated by studying the phase space near horizon of Kerr black holes, 2 while in [24] we focused on 2d dimensional and BTZ black holes [39,40] where we explicitly constructed the maximal boundary phase space.…”

“…This ambiguity may be (partially) fixed by different physical requirements. For example, this ambiguity was used in [11,12] to fix the central charge of the algebra of surface charges to a certain value, in [13][14][15][16][17] it was used to render surface charges computed at asymptotic boundaries finite and also to relate charges computed in different formulations of gravity [18,19]; see also [20,21]. In this work, as we will see the Y -ambiguity is crucially used in the charge integrability analysis.…”