Chaos, Phase Transitions and Curvature Invariants of (rotating, warped, massive) BTZ Black Holes

TL;DR

This paper explores the chaotic behavior, phase transitions, and geometric invariants of rotating, warped, massive BTZ black holes, highlighting the role of effective temperatures, thermodynamic ensembles, and curvature invariants in understanding boundary chaos.

Contribution

It clarifies how effective temperatures resolve chaos bound issues, compares phase diagrams in different gravity theories, and links boundary chaos modes to curvature invariants.

Findings

Effective temperatures help saturate chaos bounds in warped BTZ black holes.

Phase diagrams differ between topologically massive and new massive gravity theories.

Boundary modular chaos modes relate to curvature invariants.

Abstract

Combining several results from the previous works of the author, three main subtleties will be clarified here. First, similar to the rotating BTZ black holes, we show how for the warped BTZ black holes, the consideration of the effective temperatures could solve the seemingly unsaturation issue of the chaos bound. Second, comparing the Hawking-Page phase diagrams of BTZ and warped BTZ black holes in the topologically massive gravity and new massive gravity theories, we show how the characteristics of the action would specify the behaviors of the chaos modes, and there we emphasize the importance of using the local and "physical" thermodynamical ensembles for studying the boundary chaos modes in warped CFTs and also the connections with the bulk reconstruction. Third, we propose that the boundary modular scrambling modes which saturate the modular chaos bound are related to the curvature invariants in the geometrical side.