A numerical approach to particle creation in accelerating toy models

TL;DR

This paper introduces a numerical method using hyperboloidal slices to analyze particle creation during black hole formation, enabling more accurate modeling of quantum effects in dynamic spacetimes.

Contribution

It develops a novel numerical approach for studying quantum particle creation in accelerating toy models, extending analysis to both past and future null infinities.

Findings

Successfully computed particle spectra in toy models

Demonstrated the method's potential for realistic gravitational scenarios

Showed the approach's compatibility with hyperboloidal slicing techniques

Abstract

The formation of black holes by the gravitational collapse of stars is known to spontaneously excite particle pairs out of the quantum vacuum. For the canonical vacuum state at past null infinity, the expected number of particles received at future null infinity can be obtained in full closed form at sufficiently late times. However, for intermediate times, or for more complicated astrophysical processes (e.g. binary black hole mergers), the problem is technically challenging and has not yet been resolved. We develop here a numerical approach to study scattering problems of massless quantum fields in asymptotically flat spacetimes, based on the hyperboloidal slice method used in numerical relativity and perturbation theory. This promising approach can reach both past and future null infinities, and therefore it has the potential to address the Hawking scattering problem more rigorously than evolution on the usual Cauchy slices. We test this approach with some dynamical toy models in Minkowski using effective potentials that mimic the effects of gravity, and compute the spectrum of particles received at future null infinity. We finally discuss future prospects for applying this framework in more relevant gravitational scenarios.