Quantum Complexity and Holography

TL;DR

This thesis explores holographic complexity conjectures, examining their application to exotic thermodynamical systems and singular spacetimes, aiming to deepen understanding of black holes and quantum gravity.

Contribution

It reviews and extends holographic complexity proposals, analyzing their behavior in complex systems and singularities, proposing modifications and new insights into quantum gravity.

Findings

Holographic complexity can reveal universal behaviors in singular spacetimes

Modified conjectures better accommodate singularities in holographic models

Complexity dynamics may relate to classical singularity criteria

Abstract

This thesis develops recent work on the so called Volume-Complexity and Action-Complexity conjectures. According to this family of proposals, geometric quantities can be defined in some holographic gravitational theories that can be mapped with the concept of quantum complexity for states in a dual quantum-mechanical theory. In this work, we review the original motivations for the use of quantum-information theory in the search of a theory of quantum gravity, and argue in favour of holographic complexity as a promising new tool that could play a key role in the elucidation of the properties of black holes. After this introduction, we devote some time to the study of `exotic' thermodynamical systems of diverse origin, confronting the conjectures with expectations and seeking for new behaviours of holographic complexity that could help us understand or refine the existing proposals. Next, we turn our attention to the study of holographic complexity for singular spacetimes, defining slightly modified versions of the conjecture that are well adapted to singularities and searching for universal behaviours of complexity dynamics within these setups. Finally, we finish with some speculations about the relation between holographic complexity and older characterization criteria for singularities in general relativity.