Non-Gaussian ground-state deformations near a black-hole singularity

TL;DR

This paper investigates the quantum nature of black-hole singularities, showing that when probed by quantum fields, Schwarzschild black-holes appear complete, even under non-Gaussian deformations, challenging classical notions of singularity.

Contribution

It demonstrates that Schwarzschild black-holes are quantum complete when probed by self-interacting quantum fields, even with non-Gaussian deformations and excitations.

Findings

Quantum fields near the singularity have vanishing population measure.

Black-holes are complete in the quantum framework despite classical singularities.

Robustness of quantum completeness under non-Gaussian deformations.

Abstract

The singularity theorem by Hawking and Penrose qualifies Schwarzschild black-holes as geodesic incomplete space-times. Albeit this is a mathematically rigorous statement, it requires an operational framework that allows to probe the space-like singularity via a measurement process. Any such framework necessarily has to be based on quantum theory. As a consequence, the notion of classical completeness needs to be adapted to situations where the only adequate description is in terms of quantum fields in dynamical space-times. It is shown that Schwarzschild black-holes turn out to be complete when probed by self-interacting quantum fields in the ground state and in excited states. The measure for populating quantum fields on hypersurfaces in the vicinity of the black-hole singularity goes to zero towards the singularity. This statement is robust under non-Gaussian deformations of and excitations relative to the ground state. The clash of completeness cultures as exemplified with black holes is discussed.