# Finely Split Phase Transitions of Rotating and Accelerating Black Holes

## TL;DR

This paper explores the complex thermodynamic phase transitions of rotating, slowly accelerating AdS black holes, revealing new phenomena such as split transition pressures, reentrant transitions, and the absence of mini-entropic black holes in certain regimes.

## Contribution

It introduces a detailed analysis of phase behavior in rotating accelerating black holes, highlighting distinctions from non-rotating cases and identifying new phase transition phenomena.

## Key findings

- Discovery of split transition pressures and reentrant phase transitions.
- Absence of mini-entropic black holes in slow acceleration regime.
- Continuous emergence of the no black hole region from zero temperature.

## Abstract

We investigate the thermodynamic phase behaviour of rotating and slowly accelerating AdS black holes. While we find some similarities with the non-rotating charged counterparts, such as the peculiar phenomena of "snapping swallow tails" we also find subtle but significant distinctions that can be attributed to a qualitatively modified parameter space of the solution. Consequently the zeroth order phase transition now occurs over a range of pressures, mini-entropic black holes no longer exist in the regime of slow acceleration, and the "no black hole region" emerges continuously---from a zero temperature extremal black hole. The formerly equal transition pressure now experiences a fine splitting, as the emergence of a no black hole region and the zeroth-order phase transition appear at different pressures, different also from the termination pressure of the first order phase transition. This has the further effect of admitting reentrant phase transitions that can be achieved in two ways, either by varying the temperature at fixed pressure or varying the pressure at fixed temperature.