Gravitational Stress Tensor and Current at Null Infinity in Three Dimensions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909185923350528 |
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| author | Adami, H. Sheikh-Jabbari, M. M. Taghiloo, V. |
| author_facet | Adami, H. Sheikh-Jabbari, M. M. Taghiloo, V. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_00149 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gravitational Stress Tensor and Current at Null Infinity in Three Dimensions Adami, H. Sheikh-Jabbari, M. M. Taghiloo, V. High Energy Physics - Theory General Relativity and Quantum Cosmology 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. |
| title | Gravitational Stress Tensor and Current at Null Infinity in Three Dimensions |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2405.00149 |