Smooth and sharp creation of a pointlike source for a $(3+1)$-dimensional quantum field

TL;DR

This paper investigates the creation of a pointlike source for a massless scalar field in 3+1 dimensions, revealing that sharp creation leads to divergences in energy density and detector response, potentially breaking quantum correlations near black hole horizons.

Contribution

It extends previous 1+1 dimensional models to 3+1 dimensions, analyzing the singularities and energy divergences associated with smooth and sharp source creation.

Findings

Sharp creation causes divergences in energy density everywhere in the future.

Smooth creation results in infinite positive and negative energy pulses.

The process is more singular than in lower dimensions, affecting quantum correlations.

Abstract

We analyse the smooth and sharp creation of a pointlike source for a quantised massless scalar field in $(3+1)$-dimensional Minkowski spacetime, as a model for the breakdown of correlations that has been proposed to occur at the horizon of an evaporating black hole. The creation is implemented by a time-dependent self-adjointness parameter at the excised spatial origin. In a smooth creation, the renormalised energy density $\langle T_{00} \rangle$ is well defined away from the source, but it is unbounded both above and below: the outgoing pulse contains an infinite negative energy, while a cloud of infinite positive energy lingers near the fully-formed source. In the sharp creation limit, $\langle T_{00} \rangle$ diverges everywhere in the timelike future of the creation event, and so does the response of an Unruh-DeWitt detector that operates in the timelike future of the creation event. The source creation is significantly more singular than the corresponding process in $1+1$ dimensions, analysed previously, and it may be sufficiently singular to break quantum correlations as proposed in a black hole spacetime.