Thermodynamics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908720859971584 |
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| author | Fransen, Kwinten He, Temple Zurek, Kathryn M. |
| author_facet | Fransen, Kwinten He, Temple Zurek, Kathryn M. |
| contents | We compute a gravitational on-shell action of a finite, spherically symmetric causal diamond in $(d+2)$-dimensional Minkowski spacetime, finding it is proportional to the area of the bifurcate horizon $A_{\mathcal{B}}$. We then identify the on-shell action with the saddle point of the Euclidean gravitational path integral, which is naturally interpreted as a partition function. This partition function is thermal with respect to a modular Hamiltonian $K$. Consequently, we determine, from the on-shell action using standard thermodynamic identities, both the mean and variance of the modular Hamiltonian, finding $\langle K \rangle = \langle (ΔK)^2 \rangle = \frac{A_{\mathcal{B}}}{4 G_N}$. Finally, we show that modular fluctuations give rise to fluctuations in the geometry, and compute the associated phase shift of massless particles traversing the diamond under such fluctuations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22977 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thermodynamics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime Fransen, Kwinten He, Temple Zurek, Kathryn M. High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology We compute a gravitational on-shell action of a finite, spherically symmetric causal diamond in $(d+2)$-dimensional Minkowski spacetime, finding it is proportional to the area of the bifurcate horizon $A_{\mathcal{B}}$. We then identify the on-shell action with the saddle point of the Euclidean gravitational path integral, which is naturally interpreted as a partition function. This partition function is thermal with respect to a modular Hamiltonian $K$. Consequently, we determine, from the on-shell action using standard thermodynamic identities, both the mean and variance of the modular Hamiltonian, finding $\langle K \rangle = \langle (ΔK)^2 \rangle = \frac{A_{\mathcal{B}}}{4 G_N}$. Finally, we show that modular fluctuations give rise to fluctuations in the geometry, and compute the associated phase shift of massless particles traversing the diamond under such fluctuations. |
| title | Thermodynamics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2507.22977 |