Spatial dispersion of light rays propagating through a plasma in Kerr space–time

Abstract

We investigate the propagation of light through a plasma on a background Kerr spacetime via a Hamiltonian formulation. The behaviour of light when propagating through a vacuum and through a plasma is not the same; the convolution of gravitational and plasma effects gives rise to a dispersion in both space and time. The magnitude of the dispersion is a strong function of both the ray frequency and impact parameter. We discuss implications for the detection of gravitationally bent pulsar beams near the Galactic centre.

Higher order corrections to deflection angle of massive particles and light rays in plasma media for stationary spacetimes using the Gauss-Bonnet theorem

“…In particular, this family of profiles can be useful in the study of plasma environments in galaxies and galaxy-clusters. Note also, that for the case of the supermassive black hole in the center of our galaxy Sgr A*, a plasma density profile with a radial dependence of the form r −1.1 has also been considered by different authors [54,55]. Even when it is not exactly in the family described by Eqn.…”

Pulsar timing in extreme mass ratio binaries: a general relativistic approach

“…For the general plasma density distributions, where the plasma frequency, ω p (r, θ), has a spatial dependence, the Hamiltonian is not separable in terms of the usual coordinate variables and the vacuum Carter constant is no longer a constant along the geodesic, (see e.g. Perlick & Tsupko 2017;Kimpson et al 2019). In order for the equations of motion to be integrable, it is necessary for ω p to take the form,…”

“…The equations of motion therefore reduce to a problem of quadratures whereby we have four ordinary differential equations ( t, r, θ, φ) and four associated constants of motion E, L z , Q p , and H. The system of equations is integrable. It follows that the complete set of equations of motion is given, via Hamil-ton's equations, as (Kimpson et al 2019),…”

“…Due to spatial dispersion, each ray frequency also follows a different spatial path and so is subject to a different DM. We consider frequencies in the range 0.18 − 6 GHz, and use the electron number density model described in Psaltis (2012); Kimpson et al (2019).…”

“…The blue line is some illustrative circular P = 0.1 year orbit. The model for the electron number density is the same as that used in Psaltis (2012); Kimpson et al (2019)…”