Abstract
In this paper we study wave propagation and scattering near a black hole. In particular, we assume a coherent emission source near the black hole and investigate the wavefront distortion as seen by a distant observer. By ignoring the spin nature of the electromagnetic radiation we model it by a complex scalar field. Then, the propagating wave near the observer can be decomposed using the Laguerre-Gaussian mode basis and its wavefront distortion can be characterized by the decomposition coefficient. We find that this decomposition spectrum is symmetric with respect to the azimuthal quantum number in the case that the wave source is located near a nonrotating (Schwarzschild) black hole, whereas the spectrum is generically asymmetric if the host black hole is rotating (Kerr). The spectral asymmetry, or the net orbital angular momentum carried by the wave, is intimately related to the black-hole spin and mass, the wave frequency and the locations of the source and the observer. We present semianalytical expressions and numerical results for these parameter dependences. If the emitted radiation is temporally coherent, our results show that the secondary images (arising from the orbiting of the wavefront around the black hole) of the source can be almost as bright as its primary image. Separately, in the case of temporally incoherent radiation, we show that the nonfundamental spectrum components in the primary image could be resolved by spatially separated telescopes, although that would be degenerate with the telescope direction. Finally, our results suggest that the black-hole-induced spectral asymmetry is generally too weak to be observed in radio astronomy, even if the observer is located near an optical caustic.
- Received 12 April 2014
DOI:https://doi.org/10.1103/PhysRevD.90.023014
© 2014 American Physical Society