Frequency-dependent effects of gravitational lensing within plasma

Abstract: The interaction between refraction from a distribution of inhomogeneous plasma and gravitational lensing introduces novel effects to the paths of light rays passing by a massive object. The plasma contributes additional terms to the equations of motion, and the resulting ray trajectories are frequency-dependent. Lensing phenomena and circular orbits are investigated for plasma density distributions $N \propto 1/r^h$ with $h \geq 0$ in the Schwarzschild space-time. For rays passing by the mass near the plasma frequency refractive effects can dominate, effectively turning the gravitational lens into a mirror. We obtain the turning points, circular orbit radii, and angular momentum for general $h$. Previous results have shown that light rays behave like massive particles with an effective mass given by the plasma frequency for a constant density $h=0$. We study the behaviour for general $h$ and show that when $h=2$ the plasma term acts like an additional contribution to the angular momentum of the passing ray. When $h=3$ the potential and radii of circular orbits are analogous to those found in studies of massless scalar fields on the Schwarzschild background. As a physically motivated example we study the pulse profiles of a compact object with antipodal hotspots sheathed in a dense plasma, which shows dramatic frequency-dependent shifts from the behaviour in vacuum. Finally, we consider the potential observability and applications of such frequency-dependent plasma effects in general relativity for several types of neutron star.