Vacuum polarisation and regular gravitational collapse

Résumé

It is the goal of this work to revisit and revise the problem of black hole formation and evolution in semiclassical gravity—a theory in which spacetime is treated classically, while matter admits a quantum description, coupling to gravity through an expectation value of a stress-energy tensor operator. Particularly, we analyse the vacuum expectation value of this operator for a test scalar field in spherically symmetric spacetimes in which trapped regions either form or are close to forming. First, we look at the magnitude of potential corrections to the spacetime evolution in the vicinity of outer horizons formed by collapsing matter in different dynamical regimes. We find that when the matter approaches an adiabatic collapse regime while close to forming a trapped region (i.e.close to crossing its Schwarzschild radius), the vacuum energy tends to grow unboundedly. This relates to the Boulware state divergence at horizons, which in turn can be related to the existence of static horizonless BH mimicker solutions to the semiclassical Einstein equations. This suggests that the growing vacuum energy in slow collapse regimes may stabilise the matter into a final horizonless configuration...