Electric and magnetic aspects of gravitational theories

TL;DR

This thesis explores the construction of conserved electric and magnetic charges in asymptotically flat spacetimes, addressing boundary conditions, duality, and the role of NUT charge in superalgebra, advancing understanding of gravitational duality.

Contribution

It introduces a larger phase space with relaxed boundary conditions, constructs new conserved charges, and extends gravitational duality to include NUT charge within superalgebra.

Findings

Relaxed parity boundary conditions lead to new conserved charges.

Constructed magnetic dual Poincaré charges at linearized level.

Connected NUT charge with N=2 superalgebra via complexified Witten-Nester form.

Abstract

This thesis deals with the construction of conserved charges for asymptotically flat spacetimes at spatial infinity in four spacetime dimensions in a hopefully pedagogical way. As a first motivation of this work, it highlights the difficulties one encounters when trying to understand the gravitational duality, present at the linearized level, in the full non-linear Einstein's theory or even just in an asymptotic regime of it. In the first part, we restrict the discussion to the Noetherian surface charges, called "electric charges", and study the existence of a larger phase space, than previously known in the literature, where the awkward parity boundary conditions, firstly imposed by T. Regge and C. Teitelboim, are relaxed. In the absence of these parity conditions, we show how the Einstein-Hilbert action is a correct variational principle when it is supplemented by an anomalous counter-term and construct conserved and finite charges associated to the larger asymptotic symmetry group. The second and third parts focus on the magnetic information obtained through gravitational duality. As this duality is only known at the linearized level, asymptotic linearity is implicitly assumed at spatial infinity. In the second part, gravitational duality for the linearized gravity theory is reviewed and ten dual Poincar\'e charges, or topological "magnetic" charges, are constructed \`a la Abbott-Deser. The last part explains how the NUT charge N, gravitational dual of the mass M and present in the BPS bound of the supersymmetric charged Taub-NUT black hole, copes with the N=2 superalgebra. This is achieved through a complexification of the Witten-Nester 2-form.