Tall Tails of Massless Fields in Curved Spacetime

Massless fields obeying wave equations in curved spacetimes will generally propagate not only on the null cone but also within it. This is known as the “tail effect” and has been studied primarily in the context of electromagnetic and gravitational self-force. In the simplest scenario, where one point mass is responsible for all spacetime curvature and the calculations are performed in the weak field thereof, the direct detection of electromagnetic or gravitational wave tails has been argued to be difficult. However, a more recent calculation considering the weak field of an extended matter distribution suggests that gravitational tails may be imminently detectable, which would enable the realization of GRAvitational Detection And Ranging (GRADAR) for the mapping of compact matter, perhaps to unprecedented distances. To assess the generality of this finding beyond the very symmetric special case in which it was obtained, we calculate the scalar and electromagnetic wave tails directly “backscattered” from an extended body en route to a calculation of the gravitational wave tails produced in a similar manner.