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 , where denotes d‐dimensional AdS space and 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.

中文翻译：

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Schwarzschild-AdS时空和Hawking-Page相变的几何流方程

在最近观察到Ricci流和无限距离沼泽地猜想彼此密切相关之后，我们将在本文中研究AdS时空几何的几何流方程。首先，我们考虑了所谓的Yamabe流和Ricci-Bourguignon流，我们发现这两个流-与Ricci流相反-导致产品空间（如）的无限距离固定点，其中表示d维AdS空间，对应于一维球体。其次，我们考虑了AdS时空几何中的黑洞几何及其在Yamabe和Ricci-Bourguignon流下的行为。具体来说，我们将研究AdS黑洞在Ricci流，Yamabe流以及一般Ricci-Bourguignon流下是否以及如何经历Hawking-Page相变。