Hidden Symmetries in Gravity : Black holes and other minisuperspaces

Abstract

This thesis is dedicated to the study of symmetries in reduced models of gravity, with some frozen degrees of freedom. We focus on the minisuperspace reduction whith a finite number of degrees of freedom. Minisuperspaces are treated as mechanical models, evolving in one spacetime direction. This evolution parameter represents the orthogonal coordinate to the homogeneous foliation of the spacetime. I investigate their classical symmetries and the algebra of the corresponding Noether charges. After presenting the formalism allowing us to describe the reduced models in terms of an action principle, we discuss the condition for having an (extended) conformal symmetry. In particular, the black hole model enlightens the subtle role of the spacelike boundary of the homogeneous slice. The latter interplays with the conformal symmetry, being associated with a conserved quantity from the mechanical point of view. The absence of the infinite tower of charges, characteristic of the full theory, is due here to a symmetry-breaking mechanism. This is made explicit by looking at the infinite-dimensional extension of the symmetry group. This allows to look at the equation of motion of the mechanical system in terms of the infinite-dimensional group, who in turn has the effect of rescaling the coupling constants of the theory. Finally, the presence of the finite symmetry group allows defining a quantum model in terms of the corresponding representation theory. At the level of the effective theory, accounting for the quantum effects, the request that the symmetry is protected provides a powerful tool to discriminate between different modifications. In the end, the conformal invariance of the black hole background opens the door to its holographic properties and might have important consequences in the corresponding perturbation theory.

PhD thesis, 2022

References in corpus (18)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Loop Quantum Dynamics of the Schwarzschild Interior
• 3+1 Formalism and Bases of Numerical Relativity
• Polymer Quantum Mechanics and its Continuum Limit
• Notes on the BMS group in three dimensions: I. Induced representations
• Near-Horizon BMS Symmetry, Dimensional Reduction, and Black Hole Entropy
• Cosmological time and the constants of nature
• The Eisenhart lift: a didactical introduction of modern geometrical concepts from Hamiltonian dynamics
• Black hole entropy from the boundary conformal structure in 3D gravity with torsion
• Causal Structure of a recent Loop Quantum Gravity Black Hole Collapse Model
• Dark Energy and the Schwarzian Derivative
• Infinite dimensional symmetry groups of the Friedmann equations
• Hawking's information puzzle: a solution realized in loop quantum cosmology
• BMS${}_3$ Mechanics and the Black Hole Interior
• Modular polymer representations of the Weyl algebra
• From Einstein's Hole Argument to Dirac and Bergmann Observables