Researchers have developed a real-time numerical formalism to describe the spherically symmetric gravitational collapse of a scalar quantum field. This new approach employs a Pauli-Villars regulator specifically designed to cancel ultraviolet divergences in the energy-momentum tensor, including logarithmic ones, identified by covariant point splitting. The ability to handle these divergences is crucial for obtaining physically meaningful results in the study of quantum systems in strong gravitational fields.

Using this regulator, initial results show that the leading term of the entanglement entropy, which is proportional to the surface area, vanishes for a spherical region of flat spacetime. In the dynamic case of a collapsing shell of a massless scalar field, the area-normalized entropy is concentrated on the shell and maintains an approximately constant maximum value during its time evolution. This maximum value appears to be finite in the continuum limit and shows only a mild dependence on the regulator mass.

This work represents a step forward in understanding the thermodynamics of black holes and quantum information in extreme gravitational environments. The ability to simulate entanglement entropy during gravitational collapse offers a valuable tool for exploring the black hole information paradox and the nature of quantum gravity. The results suggest that the entropy associated with the formation of an event horizon could be finite and well-defined, which has profound implications for theories seeking to unify quantum mechanics and general relativity.