Critical behavior in 2+1 dimensional black holes

TL;DR

This paper investigates the critical phenomena and phase transitions of 2+1 dimensional BTZ black holes, revealing extremal black holes as critical points with unique scaling behaviors and effective spatial dimensions.

Contribution

It introduces a detailed thermodynamic analysis of BTZ black holes, identifying critical points and scaling laws, and links extremal black holes to string theory states.

Findings

Extremal spinning BTZ black holes are critical points.

Critical exponents follow first-kind scaling laws.

Effective spatial dimension of extremal black holes is one.

Abstract

The critical behavior and phase transition in the 2+1 dimensional Ba\~nados, Teitelboim, and Zanelli (BTZ) black holes are discussed. By calculating the equilibrium thermodynamic fluctuations in the microcanonical ensemble, canonical ensemble, and grand canonical ensemble, respectively, we find that the extremal spinning BTZ black hole is a critical point, some critical exponents satisfy the scaling laws of the ``first kind'', and the scaling laws related to the correlation length suggest that the effective spatial dimension of extremal black holes is one, which is in agreement with the argument that the extremal black holes are the Bogomol'nyi saturated string states. In addition, we find that the massless BTZ black hole is a critical point of spinless BTZ black holes.