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Main Authors: Tan, Hongwei, Xiao, Kui, Wang, Shoucheng
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2508.04220
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author Tan, Hongwei
Xiao, Kui
Wang, Shoucheng
author_facet Tan, Hongwei
Xiao, Kui
Wang, Shoucheng
contents This paper studies the quantization of the future null infinity ($\mathscr{I}^+$) of an asymptotically flat spacetime. Based on the observation by Ashtekar and Speziale that $\mathscr{I}^+$ can be regarded as a weakly isolated horizon, we adopt the quantization framework developed for weakly horizon to quantize $\mathscr{I}^+$. We first show that the symplectic structure of $\mathscr{I}^+$ is equivalent to the sum of the symplectic structures of two $SU(2)$ Chern-Simons theories with opposite levels. Based on this observation, we apply Chern-Simons quantization approach to quantize $\mathscr{I}^+$. Finally, we compute the entropy of $\mathscr{I}^+$ by counting the microstates, showing that it is proportional to the area of $\tildeΔ$, a spacelike cross-section of $\mathscr{I}^+$. Our result is consistent with the universal entropy formula in the framework of (weakly) isolated horizon.
format Preprint
id arxiv_https___arxiv_org_abs_2508_04220
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Null infinity as $SU(2)$ Chern-Simons theories and its quantization
Tan, Hongwei
Xiao, Kui
Wang, Shoucheng
General Relativity and Quantum Cosmology
This paper studies the quantization of the future null infinity ($\mathscr{I}^+$) of an asymptotically flat spacetime. Based on the observation by Ashtekar and Speziale that $\mathscr{I}^+$ can be regarded as a weakly isolated horizon, we adopt the quantization framework developed for weakly horizon to quantize $\mathscr{I}^+$. We first show that the symplectic structure of $\mathscr{I}^+$ is equivalent to the sum of the symplectic structures of two $SU(2)$ Chern-Simons theories with opposite levels. Based on this observation, we apply Chern-Simons quantization approach to quantize $\mathscr{I}^+$. Finally, we compute the entropy of $\mathscr{I}^+$ by counting the microstates, showing that it is proportional to the area of $\tildeΔ$, a spacelike cross-section of $\mathscr{I}^+$. Our result is consistent with the universal entropy formula in the framework of (weakly) isolated horizon.
title Null infinity as $SU(2)$ Chern-Simons theories and its quantization
topic General Relativity and Quantum Cosmology
url https://arxiv.org/abs/2508.04220