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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2410.06605 |
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| _version_ | 1866911259965784064 |
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| author | Mancilla, Robinson |
| author_facet | Mancilla, Robinson |
| contents | We derive a generalized Euler equation, $ε+p=sT+μq+y\frac{\partial p}{\partial y}$, using the effective field theory formulation of perfect fluids. This generalization was achieved by introducing a new variable $y$ into the effective action, which encodes a geometrical scale of the spacetime where the fluid is on. Notably, the generalized Euler equation is independent of the AdS/CFT correspondence. However, when applied to a holographic perfect fluid, this equation naturally recovers the Smarr formula for AdS black holes, thus situating the physical interpretation of the Smarr formula within the framework of well-established physics. Finally, our findings raise important questions regarding the validity of treating the cosmological constant $Λ$ as a thermodynamic variable, as proposed in certain frameworks within the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06605 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Euler Equation from Effective Action: Implications for the Smarr Formula in AdS Black Holes Mancilla, Robinson High Energy Physics - Theory General Relativity and Quantum Cosmology We derive a generalized Euler equation, $ε+p=sT+μq+y\frac{\partial p}{\partial y}$, using the effective field theory formulation of perfect fluids. This generalization was achieved by introducing a new variable $y$ into the effective action, which encodes a geometrical scale of the spacetime where the fluid is on. Notably, the generalized Euler equation is independent of the AdS/CFT correspondence. However, when applied to a holographic perfect fluid, this equation naturally recovers the Smarr formula for AdS black holes, thus situating the physical interpretation of the Smarr formula within the framework of well-established physics. Finally, our findings raise important questions regarding the validity of treating the cosmological constant $Λ$ as a thermodynamic variable, as proposed in certain frameworks within the literature. |
| title | Generalized Euler Equation from Effective Action: Implications for the Smarr Formula in AdS Black Holes |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2410.06605 |