Resumen de Quantum Complexity and Holography
This thesis develops recent work [1{4] on the so called Volume-Complexity and Action-Complexity conjectures. According to this family of proposals, well de ned geometric quantities can be de- ned 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 re ne the existing proposals.
Next, we turn our attention to the study of holographic complexity for singular spacetimes, de ning slightly modi ed versions of the conjecture that are well adapted to singularities and searching for universal behaviours of complexity dynamics within these setups.
Finally, we nish with some speculations about the relation between holographic complexity and older characterization criteria for singularities in general relativity
