Holographic complexity and space time locality

• Autores: Martin Sasieta Arana
• Directores de la Tesis: José Luis Fernández Barbón (dir. tes.)
• Lectura: En la Universidad Autónoma de Madrid ( España ) en 2022
• Idioma: inglés
• Número de páginas: 89
• Tribunal Calificador de la Tesis: Roberto A. Emparan García de Salazar (presid.), César Gómez López (secret.), Ben Craps (voc.)
• Programa de doctorado: Programa de Doctorado en Física Teórica por la Universidad Autónoma de Madrid
• Materias:
  • Física
    • Física teórica
• Enlaces
  • Tesis en acceso abierto en: Biblos-e Archivo
• Resumen

  • This thesis is devoted to the formulation of a new result that establishes a connection between holographic complexity in the form of the so-called Complexity = Volume proposal and the gravitational clumping of matter, within the AdS/CFT correspondence. The main result of the thesis, the ‘Momentum/Volume Complexity (PVC) correspondence’, formalizes the recurrent idea that the gravitational clumping of matter increases the complexity of the quantum state. The PVC correspondence works for perturbations of finite entropy holographic systems after scrambling, where the linear growth of complexity is associated to the frozen momentum of the excitation in the black hole interior. It generalizes previous ‘Momentum/Size’ correspondences in the literature.

    The exact PVC correspondence of this thesis works for any normalizable spherically symmetric state in arbitrary dimensions and for any normalizable state in 2+1 dimensions. Its proof is based on the kinematics of the Momentum Constraint of General Relativity.

    There are two physical obstructions for an exact PVC correspondence in more general situations. The first one is intrinsic to the topology of space, and it arises in the presence of spatial wormholes connecting different asymptotic boundaries. In this case, the spatial wormhole can stretch without any matter whatsoever. The second obstruction comes from the impossibility to define a local notion of gravitational momentum, and in particular it arises for pure gravity solutions consisting of gravitational waves. A Generalized PVC correspondence is formulated to include this latter case, derived from the Codazzi equation, which assigns a contraction of the Weyl tensor to the purely gravitational contribution of the momentum.

    The central notion of ‘infall momentum’ has a Newtonian version which explicitly captures the intuitive idea that matter clumping increases complexity. A relativistic generalization of this version also exists. Finally, the value of VC for states with small backreaction is given in terms of a radial ‘moment of inertia’ that quantifies the degree of clumping of matter.