# Thermodynamic Information Geometry and Complexity Growth of Warped AdS Black Hole and the WAdS$_3$/CFT$_2$ Correspondence

## TL;DR

This paper explores the thermodynamic geometry of warped AdS3 black holes, linking geometric stability conditions to constraints on dual CFT parameters and bulk gravitational theory.

## Contribution

It introduces a method to identify proper thermodynamic metrics and stability conditions, connecting black hole thermodynamics with dual CFT data.

## Key findings

- Identification of thermodynamic Riemannian metrics for warped AdS3 black holes
- Constraints on dual CFT central charges from thermodynamic stability
- Relations between bulk parameters and boundary theory properties

## Abstract

We study the thermodynamic properties of warped AdS$_3$ black hole within the framework of thermodynamic information geometry. Our analysis focuses on finding the set of proper thermodynamic Riemannian metrics on the space of equilibrium states, together with the conditions for local and global thermodynamic stability. We use our findings to constrain the values of left and right central charges from the dual CFT theory and the parameters of the bulk gravitational theory.