Dispersive censor of acoustic spacetimes with a shock-wave singularity

TL;DR

This paper demonstrates that quantum pressure effects in Bose-Einstein condensates prevent the formation of naked shock-wave singularities in acoustic spacetimes, effectively censoring these singularities through dispersive effects.

Contribution

It shows that microscopic dispersion in Bose-Einstein condensates removes shock-wave singularities, contrasting with classical predictions of naked singularities in fluid models.

Findings

Quantum pressure induces oscillations that regularize the spacetime

Naked shock singularities are prohibited in BECs due to dispersion

Dispersive effects act as a cosmic censorship mechanism in this context

Abstract

A dispersionless shock wave in a fluid without friction develops an acoustic spacetime singularity which is naked (not hidden by a horizon). We show that this naked nondispersive shock-wave singularity is prohibited to form in a Bose-Einstein condensate, due to the microscopic structure of the underlying ${\rm a}\!{\rm e}$ther and the resulting effective trans-Planckian dispersion. Approaching the instant of shock $t_{\rm shock}$, rapid spatial oscillations of density and velocity develop around the shock location, which begin to emerge already slightly before $t_{\rm shock}$, due to the quantum pressure in the condensate. These oscillations render the acoustic spacetime structure completely regular, and therefore lead to a removal (censoring) of the spacetime singularity. Thus, distinct from the cosmic censorship hypothesis of Penrose formulated within Einsteinian gravity, the quantum pressure in Bose-Einstein condensates censors (prohibits) the formation of a naked shock-wave singularity, instead of hiding it behind a horizon.