Скачать с ютуб Robinson Mancilla - A derivation of the Smarr formula for AdS black holes from an effective action в хорошем качестве

Robinson Mancilla - A derivation of the Smarr formula for AdS black holes from an effective action

Robinson Mancilla (University of California, Santa Barbara): A derivation of the Smarr formula for AdS black holes from an effective action The Smarr relation in AdS black hole thermodynamics is a natural generalization of the Euler equation in traditional thermodynamics. We show that the Smarr relation applies not only to AdS black holes but also to any perfect fluid living in a spacetime with a compact spatial section. This result follows naturally from an effective action that includes the size of the compact space as a thermodynamic variable, resulting in the Euler equation plus a finite size correction from where we recognize the Smarr formula. In this manner, the Smarr formula is consistent with standard ideas of Gauge/Gravity duality. Additionally, we verify the thermodynamic relations without varying the cosmological constant $\Lambda$ or Newton's constant $G_N$ for the case of the AdS Reissner-Nordström black hole. Consequently, our results argue against the proposal of extended black hole thermodynamics, where the variation of the cosmological constant is proportional to a certain thermodynamic variable.