Relativistic Rotating Electromagnetic Fields

Figure 4

The displayed peanut-like surface is an implicit plot of the vanishing of the first invariant (Equation (92)). Inside this surface, the electromagnetic field is of the magnetic type, while outside it, of the electric type, the field is of the null type on this surface. The field is of the nonpure type everywhere, except on the equatorial plane, where it is pure (). Only in a circle on the peanut’s waist, the electromagnetic field reaches the speed of light and there both invariants vanish, in agreement with Equation (16). Hence, there is no light surface, but a light circle.