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

TL;DR

This paper explores geometric flow equations like Yamabe and Ricci-Bourguignon in AdS spacetimes, analyzing their fixed points and the impact on Hawking-Page phase transitions of black holes.

Contribution

It introduces the study of Yamabe and Ricci-Bourguignon flows in AdS geometries and their effects on black hole phase transitions, extending previous Ricci flow analyses.

Findings

Yamabe and Ricci-Bourguignon flows lead to infinite distance fixed points for product spaces.

The flows influence the behavior of AdS black holes and their Hawking-Page phase transitions.

Different flows exhibit distinct effects on the stability and phase structure of black holes.

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 $AdS_d\times S^p$, where $AdS_d$ 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.