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.
Highlights
In four-dimensional gravity, the analysis of asymptotically flat spacetimes at null infinity [1, 2] has led to the Bondi mass loss formula, which states that the mass of the system decreases in time due to the emission of gravitational waves
We construct the maximal asymptotic symmetry algebra that one can obtain in two-dimensional gravity theories by imposing only partial gauge fixing on the components of the metric and very mild falloffs
After a renormalization procedure of the on-shell action and the symplectic structure involving covariant counter-terms [53, 85,86,87,88], we obtain finite charge expressions that we render integrable through a field-dependent redefinition of the symmetry parameters [12, 30, 66, 89,90,91]
Summary
In four-dimensional gravity, the analysis of asymptotically flat spacetimes at null infinity [1, 2] has led to the Bondi mass loss formula, which states that the mass of the system decreases in time due to the emission of gravitational waves. To the aforementioned higher-dimensional case, considering fluctuations of the boundary structure in lower-dimensional gravity theories unveils new asymptotic symmetries and the phase space analysis yields non-conserved and a priori nonintegrable charges at the asymptotic boundary. Analysing non-conservation, non-integrability and renormalization of the charges in two and three dimensions is definitely worthwhile since this sets the stage for similar investigations in higher dimensions Beyond these technical considerations, the boundary conditions with fluctuating boundary structure that we consider may have their own physical interest in lower-dimensional gravity theories. The boundary conditions with fluctuating boundary structure that we consider may have their own physical interest in lower-dimensional gravity theories An example where they may be relevant appears in the recent analysis of the black hole information paradox to derive the Page curve from quantum gravity path integral arguments in two dimensions [59, 60] (see [61, 62]). We conclude the discussion in the last section by providing further comments on the results
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