Abstract
The gravitational Faraday and its dual spin-Hall effects of light arise in space-times of non-zero angular momentum. These effects were studied in stationary, asymptotically flat space-times. Here we study these effects in arbitrary, non-stationary, asymptotically flat space-times. These effects arise due to interaction between light polarisation and space-time angular momentum. As a result of such interaction, the phase velocity of left- and right-handed circularly polarised light becomes different, that results in the gravitational Faraday effect. This difference implies different dynamics of these components, that begin to propagate along different paths\textemdash the gravitational spin-Hall effect of light. Due to this effect, the gravitational field splits a multicomponent beam of unpolarized light and produces polarized gravitational rainbow. The component separation is an accumulative effect observed in long range asymptotics. To study this effect, we construct uniform eikonal expansion and derive dynamical equation describing this effect. To analyse the dynamical equation, we present it in the local space and time decomposition form. The spatial part of the equation presented in the related optical metric is analogous to the dynamical equation of a charged particle moving in magnetic field under influence of the Coriolis force.
Highlights
Gravitational field affects propagation of electromagnetic waves, in particular light, in different ways
The gravitational Faraday effect is a rotation of the plane of polarization of an electromagnetic wave propagating in a stationary gravitational field, for example, near a stationary rotating black hole
Polarization to its propagation and present dynamical equations that describe the gravitational spin-Hall effect of light, which is dual to the gravitational Faraday effect
Summary
Gravitational field affects propagation of electromagnetic waves, in particular light, in different ways. By using the weak field approximation, it was shown that left- and right-handed circularly polarized light propagating near a rotating gravitational body get scattered in a different way [32,33,34,35] To consider this effect in a strong stationary gravitational field, the so-called modified geometric optics formalism was introduced [36]. To describe the gravitational Faraday and spin-Hall effects of light, we shall take the modified geometric optics approach [36] and extend it to arbitrary nonstationary asymptotically flat space-times of nonzero angular momentum [59]. We shall use geometrized units c 1⁄4 G 1⁄4 1 and conventions adopted in the book [60]
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