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

Carrington, Margaret E.; Kunstatter, Gabor; Louko, Jorma; Zhou, L. J.

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Margaret E. Carrington

Gabor Kunstatter

Professor of Mathematical Physics

L. J. Zhou


We study the creation of a spherical, finite radius source for a quantized massless scalar field in 3 þ 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 ¼ 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 ¼ a coincide for t ≤ 0 (no wall) and the two-sided Dirichlet boundary condition for t ≥ 1=λ (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 hT00i diverges to positive infinity in the outgoing energy pulse, just outside the light cone of the fully-formed wall at t ¼ 1=λ. Unlike in the 3 þ 1 point source creation, there is no persistent memory cloud of energy. As in the creation of a 1 þ 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.


Carrington, M. E., Kunstatter, G., Louko, J., & Zhou, L. J. (2018). Smooth and sharp creation of a spherical shell for a (3+1)-dimensional quantum field. Physical Review D, 98(2),

Journal Article Type Article
Acceptance Date Jun 27, 2018
Publication Date Jul 19, 2018
Deposit Date Jul 24, 2018
Publicly Available Date Jul 24, 2018
Journal Physical Review D
Print ISSN 2470-0010
Electronic ISSN 2470-0029
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 98
Issue 2
Public URL
Publisher URL


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