Localized X-shaped field generated by a superluminal electric charge

Abstract

It is now well known that Maxwell equations admit of wavelet-type solutions endowed with arbitrary group velocities (0< v(g)< infinity). 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 (SLSs), the most interesting of which are the "X-shaped" ones. The SLSs have been actually produced in a number of experiments, always by suitable interference of ordinary-speed waves. In this paper 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 in constituting a very simple example of a true X wave.