The gravitational field of a light wave

Abstract

According to the classical Einstein-Maxwell theory of gravity and electromagnetism, a light-wave traveling in empty space-time is accompanied by a gravitational field of the pp-type. Therefore point masses are scattered by a light wave, even if they carry no electric or magnetic charge, or dipole moment. In this paper I present the explicit form of the metric and curvature for both circularly and linearly polarized light, and discuss the geodesic motion of test masses. This is followed by a discussion of classical scattering of point particles by the gravitational field associated with a circularly polarized electromagnetic block wave. A generalization to a quantum theory of particles in the background of these classical wave fields is presented in terms of the covariant Klein-Gordon equation. I derive the energy spectrum of quantum particles in the specific case of the circularly polarized block wave. Finally, a few general remarks on the extension to a quantum light wave are presented.Comment: 15 pages, 2 figure

Rotation of polarization in the gravitational field of a laser beam—Faraday effect and optical activity

“…This is in agreement with the gravitational field of a polarized infinitely thin laser beam or pulse derived in [3] and the gravitational field of a polarized electromagnetic plane wave presented in [44]. However, the gravitational field in the models [3,44] does not depend on the direction of linear polarization and neither on the helicity of light in the case of circular polarization. This is in contrast to gravitational photon-photon scattering in perturbative quantum gravity discussed in [45].…”

Komar fluxes of circularly polarized light beams and cylindrical metrics

“…We conjecture that the gravitational internal solution will be the same as [6] internal solution below. To agree with [3] we write Φ for Bonnor's A which is not the electromagnetic vector potential considered above. For R ≤ a we write…”

“…We shall return to this problem after we have gained understanding from a second cylindrical system that carries a flux of angular momentum, the circularly polarized beam of light. The exact Einstein-Maxwell metric for the plane wave can be found in the literature see, for example, the fine paper [3]. However there is a problem with uniform waves that extend to infinite distance from their propagation axis.…”

Vacuum polarization in Siklos spacetimes

“…[25]). This metric can be obtained from the following one ds 2 = ±e −lr dX 2 + e 2lr (−dXdT + dY 2 ) + dr 2 (30) by imposing the coordinate transformation x = [19]. The minus and plus signs correspond to x > 0 and x < 0 regions respectively, and σ is regarded as unity for simplicity.…”

“…Another profile of this kind is H(u, x, y) = q(u)(x 2 +y 2 ) where q(u) is also arbitrary. Interestingly, the later (up to a conformal transformation) is also the wave profile of an exact gravitational wave produced by a light wave in otherwise empty spacetime [29], (see also [30]). It is also possible to generalize the Defrise metric by H(u, x, u) = j(u)x −2 , j(u) being arbitrary, which would results in different behavior compared to the ones discussed in section V. An example of Siklos spacetimes with H xy = 0 is H(u, x, y) = x 3 + 1 3 y 3 + x 2 y.…”