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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.04220 |
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| _version_ | 1866913977343148032 |
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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 |