Thermodynamics of the 3-dimensional Einstein-Maxwell system
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911925672083456 |
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| author | Miyashita, Shoichiro |
| author_facet | Miyashita, Shoichiro |
| contents | Recently, I studied the thermodynamical properties of the Einstein-Maxwell system with a box boundary in 4-dimensions [1](JHEP 04 (2024) 083). In this paper, I investigate those in 3-dimensions using the zero-loop saddle-point approximation and focusing only on a simple topology sector as usual. Similar to the 4-dimensional case, the system is thermodynamically well-behaved when $Λ<0$ (due to the contribution of the "bag of gold" saddles). However, when $Λ=0$, a crucial difference to the 4-dimensional case appears, i.e. the 3-dimensional system turns out to be thermodynamically unstable, while the 4-dimensional one is thermodynamically stable. This may offer two options for how we think about the thermodynamics of 3-dimensional gravity with $Λ=0$. One is that the zero-loop approximation or restricting the simple topology sector is not sufficient for 3-dimensions with $Λ=0$. The other is that 3-dimensional gravity is really thermodynamically unstable when $Λ=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01436 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Thermodynamics of the 3-dimensional Einstein-Maxwell system Miyashita, Shoichiro General Relativity and Quantum Cosmology High Energy Physics - Theory Recently, I studied the thermodynamical properties of the Einstein-Maxwell system with a box boundary in 4-dimensions [1](JHEP 04 (2024) 083). In this paper, I investigate those in 3-dimensions using the zero-loop saddle-point approximation and focusing only on a simple topology sector as usual. Similar to the 4-dimensional case, the system is thermodynamically well-behaved when $Λ<0$ (due to the contribution of the "bag of gold" saddles). However, when $Λ=0$, a crucial difference to the 4-dimensional case appears, i.e. the 3-dimensional system turns out to be thermodynamically unstable, while the 4-dimensional one is thermodynamically stable. This may offer two options for how we think about the thermodynamics of 3-dimensional gravity with $Λ=0$. One is that the zero-loop approximation or restricting the simple topology sector is not sufficient for 3-dimensions with $Λ=0$. The other is that 3-dimensional gravity is really thermodynamically unstable when $Λ=0$. |
| title | Thermodynamics of the 3-dimensional Einstein-Maxwell system |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2403.01436 |