Quasi-local charges and asymptotic symmetry generators

The quasi-local formulation of conserved charges through the off-shell approach is extended to cover the asymptotic symmetry generators. By introducing identically conserved currents which are appropriate for asymptotic Killing vectors, we show that the asymptotic symmetry generators can be understood as quasi-local charges. We also show that this construction is completely consistent with the on-shell method.Comment: 19 pages; v2 typos fixe

The first law of thermodynamics in Lifshitz black holes revisited

We obtain the mass expression of the three- and five-dimensional Lifshitz black holes by em- ploying the recently proposed quasilocal formulation of conserved charges, which is based on the off-shell extension of the ADT formalism. Our result is consistent with the first law of black hole thermodynamics and resolves the reported discrepancy between the ADT formalism and the other conventional methods. The same mass expression of Lifshitz black holes is obtained by using an- other quasilocal method by Padmanabhan. We also discuss the reported discrepancy in the context of the extended first law of black hole thermodynamics by allowing the pressure term.Comment: 16pages, improved version to appear in JHE

Transparentizing Black Holes to Eternal Traversable Wormholes

We present the gravity description of evaporating black holes that end up with eternal traversable wormholes where every would-be behind horizon degree is available in asymptotic regions. The transition is explicitly realized by a time-dependent bulk solution in the two-dimensional Einstein-dilaton gravity. In this solution, the initial AdS$_2$ black hole is evolved into an eternal traversable wormhole free of any singularity, which may be dubbed as transparentization of black holes to eternal traversable wormholes. The bulk construction completely matches with the boundary description governed by the Schwarzian boundary theory. We also obtain solutions describing eternal traversable wormholes as well as excitations by an additional matter and graviton oscillations on eternal traversable wormholes, which show that the eternal traversable wormhole states are gapped and non-chaotic. Embedding the 2d solution into a 4d traversable wormhole connecting two magnetically charged holes, we discuss 4d scattering of a wave incident upon one end of the traversable wormhole.Comment: 1+34 pages, 5 figures, 4 tables; v2: various typos fixed, Ref. added; v3: a few typos fixed, published versio

Thermodynamic Volume and the Extended Smarr Relation

We continue to explore the scaling transformation in the reduced action formalism of gravity models. As an extension of our construction, we consider the extended forms of the Smarr relation for various black holes, adopting the cosmological constant as the bulk pressure as in some literatures on black holes. Firstly, by using the quasi-local formalism for charges, we show that, in a general theory of gravity, the volume in the black hole thermodynamics could be defined as the thermodynamic conjugate variable to the bulk pressure in such a way that the first law can be extended consistently. This, so called, thermodynamic volume can be expressed explicitly in terms of the metric and field variables. Then, by using the scaling transformation allowed in the reduced action formulation, we obtain the extended Smarr relation involving the bulk pressure and the thermodynamic volume. In our approach, we do not resort to Euler's homogeneous scaling of charges while incorporating the would-be hairy contribution without any difficulty.Comment: 1+21 pages, plain LaTeX; v2 typo fixed and references adde