Generalized Euler Equation from Effective Action: Implications for the Smarr Formula in AdS Black Holes

2024/10/09 by Robinson Mancilla, Mancilla, Robinson · 17 citations
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Euler equations #Euler's formula #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical analysis #Mathematics #Physics #Theoretical physics #Thermodynamics

paper · pdf · doi:10.48550/arxiv.2410.06605

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2024/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We derive a generalized Euler equation, ε+p=sT+μq+y(∂ p)/(∂ 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.

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