Holographic complexity and residual entropy of a rotating BTZ black hole within Horndeski gravity

TL;DR

This paper investigates the holographic complexity and residual entropy of a rotating BTZ black hole in Horndeski gravity, revealing a non-zero minimal entropy at zero temperature that challenges classical black hole thermodynamics.

Contribution

It demonstrates that complexity and residual entropy remain non-zero at zero temperature in Horndeski gravity, providing new insights into black hole information emission and thermodynamics.

Findings

Non-zero minimal entropy at zero temperature

Complexity persists even at zero temperature

Challenges classical black hole thermodynamics

Abstract

This work explores the holographic complexity and residual entropy of a rotating BTZ black hole within the framework of Horndeski gravity. The investigation is motivated by the need to understand the emission of information from black holes, as encoded by quantum complexity, which persists even at zero temperature. Traditionally, black holes are considered to cease emitting information upon reaching zero temperature, yet our findings suggest a minimum level of information or minimal entropy. This challenges the classical notion of black hole death. Recent studies in the context of Horndeski gravity and the AdS/BCFT correspondence have identified a non-zero minimal entropy at zero temperature. Our work shows that complexity and entropy provide crucial insights into the information emission from black holes, extending beyond their classical death. These findings significantly affect our understanding of black hole thermodynamics and quantum information theory.