The Joule--Thomson and Joule--Thomson-like effects of the black holes in a cavity

Abstract

When a black hole is enclosed in a cavity in asymptotically flat space, an effective volume can be introduced, and an effective pressure can be further defined as its conjugate variable. By this means, an extended phase space is constructed in a cavity, which resembles that in the anti-de Sitter (AdS) space in many aspects. However, there are still some notable dissimilarities simultaneously. In this work, the Joule--Thomson (JT) effect of the black holes, widely discussed in the AdS space as an isenthalpic (constant-mass) process, is shown to only have cooling region in a cavity. On the contrary, in a constant-thermal-energy process (the JT-like effect), there is only heating region in a cavity. Altogether, different from the AdS case, there is no inversion temperature or inversion curve in a cavity. Our work reveals the subtle discrepancy between the two different extended phase spaces that is sensitive to the specific boundary conditions.