Flat-space Holography and Correlators of Robinson-Trautman Stress tensor

TL;DR

This paper develops a quasi-local stress tensor for four-dimensional Robinson-Trautman geometries in flat space, linking it to BMS-invariant field theory correlators through flat-space holography.

Contribution

It introduces a new stress tensor for Robinson-Trautman geometries derived from AdS solutions, enabling the study of flat-space holography and BMSFT correlators.

Findings

Correctly reproduces BMS charges from the stress tensor.

Calculates two-point functions of the stress tensor.

Calculates three-point functions of the 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.