Calculation of asymptotic charges at the critical sets of null infinity

Fuente: arXiv
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Main Author: Magdy, Mariem
Format: Preprint
Published: 2023
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author Magdy, Mariem
author_facet Magdy, Mariem
contents The asymptotic structure of null and spatial infinities of asymptotically flat spacetimes plays an essential role in discussing gravitational radiation, gravitational memory effect, and conserved quantities in General Relativity. Bondi, Metzner and Sachs established that the asymptotic symmetry group for asymptotically simple spacetimes is the infinite-dimensional BMS group. Given that null infinity is divided into two sets: past null infinity $\mathscr{I}^{-}$ and future null infinity $\mathscr{I}^{+}$, one can identify two independent symmetry groups: $\text{BMS}^{-}$ at $\mathscr{I}^{-}$ and $\text{BMS}^{+}$ at $\mathscr{I}^{+}$. Associated with these symmetries are the so-called BMS charges. A recent conjecture by Strominger suggests that the generators of $\text{BMS}^{-}$ and $\text{BMS}^{+}$ and their associated charges are related via an antipodal reflection map near spatial infinity. To verify this matching, an analysis of the gravitational field near spatial infinity is required. This task is complicated due to the singular nature of spatial infinity for spacetimes with non-vanishing ADM mass. Different frameworks have been introduced in the literature to address this singularity, e.g., Friedrich's cylinder, Ashtekar-Hansen's hyperboloid and Ashtekar-Romano's asymptote at spatial infinity. This paper reviews the role of Friedrich's formulation of spatial infinity in the investigation of the matching of the spin-2 charges on Minkowski spacetime and in the full GR setting.
format Preprint
id arxiv_https___arxiv_org_abs_2307_00318
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Calculation of asymptotic charges at the critical sets of null infinity
Magdy, Mariem
General Relativity and Quantum Cosmology
Mathematical Physics
The asymptotic structure of null and spatial infinities of asymptotically flat spacetimes plays an essential role in discussing gravitational radiation, gravitational memory effect, and conserved quantities in General Relativity. Bondi, Metzner and Sachs established that the asymptotic symmetry group for asymptotically simple spacetimes is the infinite-dimensional BMS group. Given that null infinity is divided into two sets: past null infinity $\mathscr{I}^{-}$ and future null infinity $\mathscr{I}^{+}$, one can identify two independent symmetry groups: $\text{BMS}^{-}$ at $\mathscr{I}^{-}$ and $\text{BMS}^{+}$ at $\mathscr{I}^{+}$. Associated with these symmetries are the so-called BMS charges. A recent conjecture by Strominger suggests that the generators of $\text{BMS}^{-}$ and $\text{BMS}^{+}$ and their associated charges are related via an antipodal reflection map near spatial infinity. To verify this matching, an analysis of the gravitational field near spatial infinity is required. This task is complicated due to the singular nature of spatial infinity for spacetimes with non-vanishing ADM mass. Different frameworks have been introduced in the literature to address this singularity, e.g., Friedrich's cylinder, Ashtekar-Hansen's hyperboloid and Ashtekar-Romano's asymptote at spatial infinity. This paper reviews the role of Friedrich's formulation of spatial infinity in the investigation of the matching of the spin-2 charges on Minkowski spacetime and in the full GR setting.
title Calculation of asymptotic charges at the critical sets of null infinity
topic General Relativity and Quantum Cosmology
Mathematical Physics
url https://arxiv.org/abs/2307.00318