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UMR 5672

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Soutenance de Francesco Sartini

Hidden Symmetries in Gravity: Black holes and other minisuperspaces
When Jul 01, 2022
from 09:00 to 11:00
Where Salle Condorcet (1 place de l'école)
Contact Name Francesco Sartini
Attendees Francesco Sartini
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This thesis is dedicated to the study of symmetries in reduced models of gravity, with some frozen degrees of freedom. In particular, we focus on the minisuperspace reduction where the number of remaining degrees of freedom is finite. This work takes its place in the quest of understanding the role of physical and gauge symmetries in gravity. The minisuperspaces are treated as mechanical models, evolving in one spacetime direction, and I investigate their classical symmetries and the algebra of the corresponding Noether charges, showing the existence of an extended conformal symmetry.

In particular, focusing on the black hole model, we enlighten 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. In particular, this allows looking 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 the definition of a quantum model in terms of the representation theory of the symmetry group. 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 the study of its holographic properties and might have important consequences on the study of the propagation of test fields on it and the corresponding perturbation theory.