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

TL;DR

This paper models the dynamic formation of a spherical shell in a 3+1 dimensional quantum field, analyzing energy pulses and detector responses to assess implications for black hole horizon physics.

Contribution

It introduces a novel self-adjoint extension approach to simulate shell creation, revealing finite detector responses and diverging energy densities, challenging firewall formation theories.

Findings

Energy density diverges outside the light cone of the shell

Detector response remains finite and time-scale independent

No persistent energy memory cloud after shell formation

Abstract

We study the creation of a spherical, finite radius source for a quantized massless scalar field in 3+1 dimensions. The goal is to model the breakdown of correlations that has been proposed to occur at the horizon of an evaporating black hole. We do this by introducing at fixed radius $r=a$ a one parameter family of self-adjoint extensions of the three dimensional Laplacian operator that interpolate between the condition that the values and the derivatives on the two sides of $r=a$ coincide for $t\le0$ (no wall) and the two-sided Dirichlet boundary condition for $t \ge 1/\lambda$ (fully-developed wall). Creation of the shell produces null, spherical pulses of energy on either side of the shell, one ingoing and the other outgoing. The renormalized energy density $\langle T_{00}\rangle$ diverges to positive infinity in the outgoing energy pulse, just outside the light cone of the fully-formed wall at $t=1/\lambda$. Unlike in the 3+1 point source creation, there is no persistent memory cloud of energy. As in the creation of a 1+1 dimensional wall, the response of an Unruh-DeWitt detector in the post-shell region is independent of the time scale for shell formation and is finite. The latter property casts doubt on the efficacy of this mechanism for firewall creation.