Quantum correlations in a gravitational collapse simulation with SpheriCo.jl

TL;DR

This paper introduces SpheriCo.jl, a new computational tool for simulating gravitational collapse of scalar fields, including quantum effects, revealing critical behavior and correlations across horizons.

Contribution

The paper presents a novel code capable of simulating both classical and quantum scalar field collapse with enhanced stability and accuracy, enabling new insights into quantum correlations in gravitational collapse.

Findings

Successful simulation of classical gravitational collapse showing expected critical behavior.

First computations of two-point correlation functions indicating non-trivial correlations across horizons.

Enhanced numerical stability allowing longer and more detailed simulations.

Abstract

We report on work using a newly developed code, SpheriCo.jl, that computes the gravitational collapse of a spherical scalar field, where the scalar can be either a classical field, or a quantum field operator. By utilising summation-by-parts methods for the numerical derivatives we are able to simulate the collapse longer than was possible previously due to enhanced numerical stability. We present a suite of tests for the code that tests its accuracy and stability, both for the classical and quantum fields. We are able to observe critical behavior of gravitational collapse for the classical setup, in agreement with expected results. The code is also used to compute two-point correlation functions, with results that hint at a non-trivial correlation across the horizon of Hawking quanta.