Flat-space holography and correlators of Robinson–Trautman stress tensor

Abstract

We propose a quasi-local stress tensor for the four-dimensional asymptotically flat Robinson-Trautman geometries by taking the flat-space limit from the corresponding asymptotically AdS solutions. This stress tensor results in the correct charges of the generators of BMS symmetry if we define conformal infinity by an anisotropic scaling of the metric components. Using flat-space holography this stress tensor is related to expectation values of the stress tensor in a dual field theory called BMS-invariant field theory (BMSFT). We also calculate the two and three point functions of the proposed stress tensor.

First law of entanglement entropy in flat-space holography

“…Our proposal is that this surface for the flat spacetimes is the same as that one for the asymptotically AdS case whose flat-space limit yields the asymptotically flat spacetimes [30]. This proposal works again in this problem similar to all previous works [33]- [38], however, a thorough investigation is necessary that we hope to do in our future studies.…”

“…However, such a definition for conformal infinity of asymptotically flat spacetimes is not appropriate in the flat-space holography . In the previous works [30], [33]- [38], in the flatspace holography, Σ has been defined by using the corresponding surface of asymptotically AdS spacetimes which their flat-space limit yields the asymptotically flat metric. To be precise, let us consider AdS 3 metric written in the BMS coordinate,…”

“…In the AdS/CFT correspondence, the metric of Σ in (3.33) is given by using (3.36). The new point in all of papers [30], [33]- [38] is that (3.36) is also appropriate for writing metric of Σ in the ℓ → ∞ limit. The proposal of [30] for the definition of Σ is that we use a metric similar to (3.36) but replace ℓ with three dimensional Newton constant G. In this paper we employ this definition of Σ.…”

General null asymptotics and superrotation-compatible configuration spaces in d ≥ 4

“…Among the four-dimensional spacetimes with a time-dependent h (0)AB , which are not asymptotically flat in the usual sense -but nonetheless locally possess null infinity -Robinson-Trautman spacetimes [76] are particularly relevant in the theory of gravity waves. In the broader context of holography with negative cosmological constant and its relations with Ricci-flat holography, four dimensional AdS-Robinson-Trautman spacetimes have been discussed as dual of out of equilibrium phenomena [77] and a flat limit was taken in [78]. Higher dimensional Robinson-Trautman spacetimes with any value of the cosmological constant have been defined in [79] (see (4.37)).…”

“…Despite the points raised here, which are to be critically revised in order to push the scattering picture [5] to higher dimensions, if we limit ourselves to local considerations of Ricci-flat asymptotics, we can hope to relate the configuration spaces here discussed with AdS/CFT in the spirit of de Boer and Solodukhin [96] or a flat limit approach in the spirit of [38,39,78,83,84,97]. We have envisaged in subsection 3.2.3 an interpretation of the leading logarithmic term appearing in the expansion of h AB in terms of anomalies of the dual field theory, which we plan to analyse further [67].…”