Seminario

Il giorno 18 novembre alle ore 14,00 presso l'aula 412, Leonardo Modesto (Università di Cagliari) terra' un seminario dal titolo

Quantum Gravity and Superconductive Spacetime

Abstract

I will discuss a trinity of interconnected topics: quantum liquefaction in curved spacetime, spacetime singularities, and quantum gravity.
I will start with QFT in curved spacetime and show that Bogoliubov transformations can be expressed in terms of a unitary squeezing operator, thereby guaranteeing the unitarity of the S-matrix in a general spacetime. It follows that the Bogoliubov vacuum is a BCS-like state: an electron-positron condensate for fermions, and a Bose–Einstein condensate for bosons. Gravity thus turns the vacuum into a many-body condensate with respect to which quantum evolution remains unitary. By reverse engineering, we construct the effective Hamiltonian in a black hole background with a mass-gap function growing approximately linearly with temperature. The Hawking state is therefore exactly a BCS state, and the entanglement entropy is recovered, satisfying the area law from formation to full evaporation.

Crucially, however, this unitarity argument assumes geodesic completeness, namely the absence of spacetime singularities. To address this, we turn to nonlocal quantum gravity, compatible with classical and quantum stability, perturbative unitarity, causality, and quantum finiteness. The latter implies Weyl invariance at both classical and quantum levels, placing the theory in the spontaneously broken phase of conformal symmetry. We show that this symmetry resolves the black hole singularity problem, yielding singularity-free exact solutions that are geodesically complete: neither massive nor massless particles can reach the former singularity in finite proper time or affine parameter.