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arXiv · 2405.00149

Gravitational Stress Tensor and Current at Null Infinity in Three Dimensions

H. Adami·M. M. Sheikh-Jabbari·V. Taghiloo
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Abstract

We develop the framework that reveals the intrinsic conserved stress tensor and current associated with the null infinity of a three-dimensional ($3d$) asymptotically flat spacetime. These are, respectively, canonical conjugates of degenerate metric and Ehresmann connection of the boundary Carrollian geometry. Their conservation reproduces the Bondi-mass and angular momentum conservation equations if the asymptotic boundary is endowed with a torsional affine connection that we specify. Our analysis and results shed further light on the $3d$ flat holography; the stress tensor and current give rise to an asymptotically flat fluid/gravity correspondence. The requirement of a well-defined $3d$ action principle yields Schwarzian action at null infinity governing the dynamics induced by reparametrizations over the celestial circle, in accord with the codimension $2$ holography of $3d$ flat spacetimes.

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H. Adami, M. M. Sheikh-Jabbari, V. Taghiloo. 2024-04-30. Gravitational Stress Tensor and Current at Null Infinity in Three Dimensions. https://arxiv.org/abs/2405.00149

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