Nonthermal nature of extremal Kerr black holes

TL;DR

Extremal Kerr black holes, like extremal Reissner-Nordstrom black holes, do not exhibit thermal behavior, lacking a well-defined temperature or entropy, as shown by extending previous analysis.

Contribution

This paper extends the nonthermal analysis of extremal black holes from Reissner-Nordstrom to Kerr black holes, demonstrating their similar nonthermal nature.

Findings

Extremal Kerr black holes lack a well-defined temperature.

Thermodynamic entropy is undefined for extremal Kerr black holes.

The nonthermal behavior is consistent across different types of extremal black holes.

Abstract

Liberati, Rothman and Sonego have recently showed that objects collapsing into extremal Reissner-Nordstrom black holes do not behave as thermal objects at any time in their history. In particular, a temperature, and hence thermodynamic entropy, are undefined for them. I demonstrate that the analysis goes through essentially unchanged for Kerr black holes.