Symmetries and conservation laws in Lagrangian gauge theories with applications to the mechanics of black holes and to gravity in three dimensions

TL;DR

This paper develops a formalism for conservation laws in Lagrangian gauge theories, applies it to black hole thermodynamics in various dimensions, and explores asymptotic symmetries and charges relevant to quantum gravity in three dimensions.

Contribution

It introduces a self-consistent formalism for conservation laws in gauge theories and applies it to black hole thermodynamics and asymptotic symmetries in three-dimensional gravity.

Findings

Thermodynamics of black holes, strings, and rings analyzed.

New black hole solutions with closed timelike curves described.

Asymptotic symmetry algebra with central extensions constructed.

Abstract

The treatment of exact conservation laws in Lagrangian gauge theories constitutes the main axis of the first part of the thesis. The formalism is developed as a self-consistent theory but is inspired by earlier works, mainly by cohomological results, covariant phase space methods and by the Hamiltonian formalism. The thermodynamical properties of black holes, especially the first law, are studied in a general geometrical setting and are worked out for several black objects: black holes, strings and rings. Also, the geometrical and thermodynamical properties of a new family of black holes with closed timelike curves in three dimensions are described. The second part of the thesis is the natural generalization of the first part to asymptotic analyses. We start with a general construction of covariant phase spaces admitting asymptotically conserved charges. The representation of the asymptotic symmetry algebra by a covariant Poisson bracket among the conserved charges is then defined and is shown to admit generically central extensions. The asymptotic structures of three three-dimensional spacetimes are then studied in detail and the consequences for quantum gravity in three dimensions are discussed.