Dispersive censor of acoustic spacetimes with a shock-wave singularity

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 $\mathrm{a}\mathrm{e}$ther and the resulting effective trans-Planckian dispersion. Approaching the instant of shock $t_{\mathrm{shock}}$, rapid spatial oscillations of density and velocity develop around the shock location, which begin to emerge already slightly before $t_{\mathrm{shock}}$, 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.

11 pages, 7 figures

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• Quantum nonlinear effects in the number-conserving analogue gravity of Bose-Einstein condensates
• Analog charged black hole formation via percolation: Exploring cosmic censorship and Hoop conjecture
• Acoustic Analogues of Extremal Rotating Black Holes in Exciton-Polariton Condensates
• Probing Penrose-type singularities in sonic black holes