The X - shaped , localized field generated by a Superluminal electric charge ( † )

It is now wellknown that Maxwell equations admit of wavelet-type solutions endowed with arbitrary group-velocities (0 < vg <∞). Some of them, which are rigidly moving and have been called localized solutions, attracted large attention. In particular, much work has been done with regard to the Superluminal localized solutions (SLS), the most interesting of which resulted to be the “X-shaped” ones. The SLSs have been actually produced in a number of experiments, always by suitable interference of ordinaryspeed waves. In this note we show, by contrast, that even a Superluminal charge creates an electromagnetic X-shaped wave. Namely, on the basis of Maxwell equations, we are able to evaluate the field associated with a Superluminal charge (under the approximation of pointlikeness): it results to constitute a very simple example of true X-wave. PACS nos.: 03.50.De ; 03.30.+p ; 41.20;Jb ; 04.30.Db .