These two situations are illustrated below,
In both cases energy oscillates between two space dimensions. In both cases the particle travels at light speed, \(c\) down both \(t_g\) and \(t_c\) time axis. However, one exist in the charge time dimension, \(t_c\), and its velocity in space is defined as,
\(v_1=\cfrac{d\,x_1}{d\,t_c}\) and \(v_2=\cfrac{d\,x_2}{d\,t_c}\)
The other exist in gravitational time dimension, \(t_g\) and its velocity in space is defined as,
\(v_1=\cfrac{d\,x_1}{d\,t_g}\) and \(v_2=\cfrac{d\,x_2}{d\,t_g}\)
An possible example of such a radiator, a particle that is a wave without being at light speed in space is temperature or heat.
In which case, two hot spots \(x_1\) and \(x_2\) does not achieve thermal equilibrium but energy oscillates between them. There will be two types of heat, one that exist in charge time and is associated with the charge, \(q\) and electrostatic phenomenon, and another in gravitational time associated with mass, \(m\) and gravitation phenomenon.
It may just be a misnomer to call both 'time' waves (as they propagating on the \(t_c\) or \(t_g\) time axis), heat. Even to identify them as heat could be wrong.
It is most important to note that only two space dimensions are involved, that means these 'time' waves are two dimensional phenomena. Flat heat, which suggests that we would model heat flow as lamina flow of infinitely thin sheets.
