Vacuum Cherenkov effect in logarithmic nonlinear quantum theory

We describe the radiation phenomena which can take place in the physical vacuum such as Cherenkov-type shock waves. Their macroscopical characteristics - cone angle, flash duration, radiation yield and spectral distribution - are computed. It turns out that the radiation yield is proportional to the square of the proper energy scale of the vacuum which serves also as the vacuum instability threshold and the natural ultraviolet cutoff. While the analysis is mainly based on the theory engaging the logarithmic nonlinear quantum wave equation, some of the obtained results must be valid for any Lorentz-invariance violating theory describing the vacuum by (effectively) continuous medium in the long-wavelength approximation. -- Highlights: The Cherenkov-type shock waves can take place in the physical vacuum. → Their macroscopical characteristics, cone angle, flash duration, radiation yield and spectral distribution, are computed. → The radiation yield is proportional to the square of the proper energy of the vacuum.