Cerenkov radiation emitted by charged particles in a gravitational field

Charged particles propagating in an external gravitational field with negative Ricci tensor components can emit radiation by the Cerenkov process. The external gravitational field acts like an effective refractive index for light. Such a negative Ricci tensor arises in the core of cosmic strings owing to the negative pressure along the string axis. Cosmic ray protons moving along the core of cosmic strings emit Cerenkov radiation with a characteristic spectrum which can be used as a signal for the detection of cosmic strings. Another example of a metric with negative Ricci curvature is the gravitational field of galactic dark matter. We derive the expressions for the gravitational Cerenkov radiation of charged particles for these metrics.