标题： 霍金-佩奇相变中的新双重关系和常数 显示英文标题

标题： Novel dual relation and constant in Hawking-Page phase transitions

摘要： 普遍关系和常数在理解物理理论中具有重要的应用。 在本文中，我们探讨了施瓦茨希尔德反德西特黑洞中的霍金-佩奇相变问题。 我们发现($d$+1)维黑洞的最低温度与$d$维中的霍金-佩奇相变温度之间存在一种新的精确对偶关系，这让人联想到全息原理。 此外，我们发现，在霍金-佩奇转变点，归一化的鲁佩纳尔标量曲率是一个普遍常数。 由于鲁佩纳尔曲率可以被视为黑洞微观结构之间相互作用强度的指示器，我们推测这个普遍常数表示一个相互作用阈值，超过该阈值后，虚拟黑洞会变为真实黑洞。 这种新的对偶关系和普遍常数在理解霍金-佩奇相变中是基本的，并可能在未来在黑洞物理中具有新的重要应用。 显示英文摘要

摘要： Universal relations and constants have important applications in understanding a physical theory. In this article, we explore this issue for Hawking-Page phase transitions in Schwarzschild anti-de Sitter black holes. We find a novel exact dual relation between the minimum temperature of the ($d$+1)-dimensional black hole and the Hawking-Page phase transition temperature in $d$ dimensions, reminiscent of the holographic principle. Furthermore, we find that the normalized Ruppeiner scalar curvature is a universal constant at the Hawking-Page transition point. Since the Ruppeiner curvature can be treated as an indicator of the intensity of the interactions amongst black hole microstructures, we conjecture that this universal constant denotes an interaction threshold, beyond which a virtual black hole becomes a real one. This new dual relation and universal constant are fundamental in understanding Hawking-Page phase transitions, and might have new important applications in the black hole physics in the near future.