New approach to electromagnetic wave tails on a curved spacetime

We present an alternative method for constructing the exact and approximate solutions of electromagnetic wave equations whose source terms are arbitrary order multipoles on a curved spacetime. The developed method is based on the higher-order Green’s functions for wave equations which are defined as distributions that satisfy wave equations with the corresponding order covariant derivatives of the Dirac delta function as the source terms. The constructed solution is applied to the study of various geometric effects on the generation and propagation of electromagnetic wave tails to first order in the Riemann tensor. Generally the received radiation tail occurs after a time delay which represents geometrical backscattering by the central gravitational source. It is shown that for an arbitrary weak gravitational field it is valid that the truly nonlocal wave-propagation correction (the tail term) has a universal form which is independent of multipole structure of the gravitational source. In a particular case when the electromagnetic radiation pulse is generated by the wave source during a finite time interval, the structure of the wave tail at the time after the direct pulse has passed the gravitational source is in the first approximation independent of the higher multipole moments of the source of gravitation, including the angular momentum. These results are then applied to a compact binary system. It follows that under certain conditions the tail energy can be a noticeable fraction of the primary pulse energy; namely, it is shown that for a particular model the energy carried away by the tail can amount to 10% of the energy of the low-frequency modes of the direct pulse. The present results indicate that the wave tails should be carefully considered in energy calculations of such systems and that the delay effect of the wave tails may be of great importance for their observational detection.