Algebraic structure of general electromagnetic fields and energy flow

The algebraic structures of a general electromagnetic field and its energy–momentum tensor in a stationary space–time are analyzed. The explicit form of the reference frame in which the energy of the field appears at rest is obtained in terms of the eigenvectors of the electromagnetic tensor and the existing Killing vector. The case of a stationary electromagnetic field is also studied and a comparison is made with the standard short-wave approximation. The results can be applied to the general case of a structured light beams, in flat or curved spaces. Bessel beams are worked out as example.

► Algebraic structure of general electromagnetic fields in stationary spacetime. ► Eigenvalues and eigenvectors of the electomagnetic field tensor. ► Energy–momentum in terms of eigenvectors and Killing vector. ► Explicit form of reference frame with vanishing Poynting vector. ► Application of formalism to Bessel beams.