Cherenkov radiation as ghost instability

TL;DR

The paper investigates the relationship between Cherenkov radiation and ghost instabilities in modified gravity theories. It develops a general kinematic framework showing that Cherenkov emission and vacuum decay with negative-energy ghosts are two faces of the same process, sharing a common energy-momentum conservation structure. The analysis spans 1+1 to higher dimensions, revealing how dimensionality shapes the emission cone and the corresponding ghost decay channels, with 2D enabling a Cherenkov cone and 1+1D allowing multi-particle analogues. The work highlights the role of UV cutoffs and background structure in regulating the instability and points to potential observational signatures and future avenues for exploring quasi-stable configurations in gravitational contexts.

Abstract

We demonstrate that Cherenkov radiation can be interpreted as ghost instability of a certain type. Solutions of modified gravity theories often contain ghost instabilities. One type of such ghost instability is associated with existence of different types of species with causal cones that do not share common time, which leads to vacuum decay via creation of particles with positive and negative energies. We show that this ghost instability can be seen as Cherenkov radiation and vice versa.

Figures (5)

• Figure 1: On the left plot the cone of propagation (blue) of the perturbations of the medium, and the momentum vector of propagation of a particle propagating at a subsonic (dotted red), sonic (solid red) and supersonic (dashed red) speed, are shown. The corresponding dispersion relations are depicted on the right plot. When the velocity of the particle becomes equal to the speed of phonons, Cherenkov radiation occurs. The particle looses its energy and momentum (red solid arrow) by creating a phonon (blue arrow).
• Figure 2: The dispersion relation for the phonons of the medium, shown by the cone, and the tangential plane to the mass surface of the massive particle, moving through the medium at the speed higher than the speed of perturbations, in 2+1 dimensions. The intersection of the two surfaces, shown by blue lines, corresponds to the kinematically allowed values of the momenta and energy of emitted phonons. The red lines indicate the corresponding change in momentum of the moving particle. The projection of blue lines to the $\{k_x,k_y\}$ plane gives the direction of propagation of Cherenkov radiation, which corresponds to the Cherenkov angle.
• Figure 3: Three different mutual configurations of cones are shown. On the left plot the cones have a common Cauchy surface as well as common time, therefore there is no vacuum decay. On the right plot the cones do not have a common time, therefore the energy of the system of two fields is not positive definite, so that vacuum decay is possible. The middle plot is the marginal case, when the cones just touch each others from outside. In this case the vacuum decay just becomes possible.
• Figure 4: The dispersion relations corresponding to the situations depicted in Fig. \ref{['fig_cones']}. On the left figure, the energy of the red particle can be negative, however, the vacuum decay is kinematically forbidden. On the right plot the vacuum decay is possible. The middle plot is the marginal case, when the vacuum decay starts.
• Figure 5: The cones corresponding to the dispersion relations of the two species, a 2+1 analogue of the right plot of the Fig. \ref{['fig_dispersion']}. The particle with positive energy is represented by the blue cone, while the ghost particle is shown by orange. The intersection of the ghost cone with the past photon cone, shown by red lines, corresponds to the kinematically allowed values of the momenta of created ghost particles. The production of the ghost particles is accompanied by creation of phonons, shown by blue lines on the blue future cone. The projection of these lines to the $\{k_x,k_y\}$ plane gives the direction of propagation of created phonons and ghost particles, which is similar to the Cherenkov cones of radiation.