Aspects of Quantum Gravity: From Black Hole Thermodynamics to Holography

Abstract

Understanding the nature of quantum gravity remains one of the cutting-edge challenges in modern theoretical physics. Despite widespread interest and extensive research, the formulation of a complete theory of quantum gravity remains an unsolved problem. This thesis aims to explore quantum gravity from two primary perspectives: black hole thermodynamics and holography.

Black hole chemistry extends black hole thermodynamics by incorporating the cosmological constant, treating the black hole mass as enthalpy rather than energy, and interpreting the cosmological constant and its conjugate variable as pressure and volume, respectively. Holographic complexity investigates the duality between gravitational quantities in the bulk and quantum complexity on the boundary. This includes various proposals such as complexity=volume (CV), complexity=spacetime volume (CV2.0), complexity=action (CA), and complexity=anything proposals.

In our exploration of black hole thermodynamics, we investigate phase transitions near quadruple points, where four distinct black hole phases coexist. Utilizing the free-energy landscape technique within the framework of four-dimensional Einstein gravity coupled with nonlinear electrodynamics (NLE), we undertake the first investigation into the dynamics of recently discovered multicriticality in black holes. By treating off-shell Gibbs free energy as a potential and solving the Smoluchowski equation numerically, we capture the evolution of the state probability distributions during black hole phase transitions. Our study reveals how off-shell Gibbs free energy, shaped by ensemble temperatures, influences these transitions and highlights intricate behaviours such as weak and strong oscillations.

In our investigation of holography, we analyze the complexity of conformal field theories (CFTs) compactified on a circle with a Wilson line, corresponding to magnetized solitons in four-dimensional and five-dimensional Anti-de Sitter space (AdS). We explore three distinct proposals for holographic complexity. Our study reveals that these proposals exhibit a confinement-deconfinement phase transition driven by variations in the Wilson line, with the complexity of formation acting as the order parameter for this transition. We find that the proposed volume and action complexity functionals obey a scaling relation with the radius of the circle. We show that this scaling law is applicable to a broad family of potential complexity functionals and conjecture that the scaling law applies to the complexity of conformal field theories on a circle in more general circumstances.