Transition radiation from motion of electrons in curved space

Čerenkov radiation has hinted people since its birth as a basic observable phenomenon to unfold energy transfer from kinetic energy of moving electrons to electromagnetic waves, evanescent or traveling, whose physical principle is shared by transition radiation and Bremsstrahlung as well; whereas an emergent Transformation Optics strategy¹ provides such a possibility, as enabling manipulation of light flow arbitrarily. Invariance form of Maxwell´s equations, under various coordinates, including curvilinear, guarantees light to behave according to man´s design, shaped by curved electromagnetic space.