Geometric Flow Equations for Schwarzschild-AdS Space-time and Hawking-Page Phase Transition

Abstract

Following the recent observation that the Ricci flow and the infinite distance swampland conjecture are closely related to each other, we will investigate in this paper geometric flow equations for AdS space-time geometries. First, we consider the so called Yamabe and Ricci-Bourguignon flows and we show that these two flows - in contrast to the Ricci flow - lead to infinite distance fixed points for product spaces like $Ad{S}_d\times S^p$, where $Ad{S}_d$ denotes d-dimensional AdS space and $S^p$ corresponds to a p-dimensional sphere. Second, we consider black hole geometries in AdS space time geometries and their behaviour under the Yamabe and Ricci-Bourguignon flows. Specifically we will examine if and how the AdS black holes will undergo a Hawking-Page phase transition under the Ricci flow, the Yamabe flow and under the general Ricci-Bourguignon flow.

arXiv comment35 pages, one additional reference in revised version

References in corpus (6)

• On the Geometry of the String Landscape and the Swampland
• The Swampland: Introduction and Review
• AdS and the Swampland
• Ricci flow and black holes
• Infinite Black Hole Entropies at Infinite Distances and Tower of States
• Swampland, Gradient Flow and Infinite Distance

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• The Black Hole Entropy Distance Conjecture and Black Hole Evaporation
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• Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity
• On the dual relation in the Hawking--Page phase transition of the black holes in a cavity
• Geometric Flow of Bubbles
• Nonassociative Ricci flows, star product and R-flux deformed black holes, and swampland conjectures
• Geometric flow equations for the number of space-time dimensions
• The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories