Holographic Complexity and Phase Transition for AdS Black Holes

TL;DR

This paper explores the generalized volume-complexity in AdS black holes, revealing universal phase transition behaviors and the impact of effective potential peaks, extending the understanding of holographic complexity.

Contribution

It investigates generalized volume-complexity for black holes with multiple horizons, identifying universal features and phase transition patterns not previously detailed.

Findings

Turning time is universal and horizon-independent.

Multiple phase transitions can occur depending on potential peaks.

Generalized volume-complexity relates to the shape of the effective potential.

Abstract

Recently, the complexity equals any gravitational observable conjecture has been proposed in [Phys. Rev. Lett. 128, 081602 (2022)], which is an extension of the complexity equals volume proposal. These gravitational observables are referred to as generalized volumes. In this paper, we investigate the generalized volume-complexity for black holes with one or two horizons respectively. We verify that the turning time is universal and independent of the Cauchy horizon. Not only does this phase transition occur once, but it may also occur two or more times depending on the number and height of the effective potential peaks. On the other hand, we confirm that the generalized volume-complexity can be divided based on the shape of the effective potential. We then discuss the non-smooth transition from the Reissner-Nordstr\"om-AdS black hole to the Schwarzschild-AdS black hole.