The gravitational field of a spinning pencil of light

Abstract

An exact solution of Einstein’s equations in a vacuum (outside of singularities), belonging to Kundt’s class and Petrov type N, is interpreted as the metric of a spinning pencil of light (a linear source infinitely extended in one direction and moving with the speed of light). It is shown that the gravitational fields of two parallel pencils of light do not interact with each other, i.e., the superposition of the metrics of two parallel pencils of light is an exact solution of Einstein’s equations in a vacuum.

The gravitational field of photons

“…In Sects. 3 and 4 I shall examine the gravitational field represented by metric (1) (or (8)) with A given by (6), and I shall do this in two ways. First, I shall find the physical components of the Riemann tensor, and, secondly, I shall consider the radial force on a test particle held at rest in the field.…”

“…The gravitational properties of photons can be illustrated by considering the metric for a steady beam [2][3][4][5][6]. It is interesting to compare this with the Levi Civita solution for an infinite static material rod, the peculiarities of which are well known [7,8].…”

The gravitational field of a laser beam beyond the short wavelength approximation

“…The statement of [36] by Tolman et al that a non-divergent light beam does not deflect gravitationally a co-directed parallel light beam has been recovered in different contexts: two codirected parallel cylindrical light beams of finite radius [3,4,24], spinning non-divergent light beams [23], non-divergent light beams in the framework of gravito-electrodynamics [13], parallel co-propagating light-like test particles in the gravitational field of a 1D light pulse [26]. In fourth order in the divergence angle, we found a deflection of parallel co-propagating test beams.…”

“…This corresponds to the short wavelength limit where all wavelike properties of light are neglected. Further studies of the gravitational field of light that share this feature include the investigation of two co-directed parallel cylindrical light beams of finite radius [3,24], spinning non-divergent light beams [23], non-divergent light beams in the framework of gravito-electrodynamics [13], and the gravitational field of a point like particle moving with the speed of light [1,38].…”

Effects of Non-locality in Gravity and Quantum Theory

“…Later, Bonnor studied extensively the gravitational field of null fluids and spinning pencils of light [204][205][206], see also Refs. [207][208][209]. These studies have been generalized to higher dimensions [210,211], to incldue electric charge [212], in other asymptotic geometries [213,214] as well as in supergravity [215].…”