Can a circulating light beam produce a time machine?

Abstract

In a recent paper, Mallett found a solution of the Einstein equations in which closed timelike curves (CTC's) are present in the empty space outside an infinitely long cylinder of light moving in circular paths around an axis. Here we show that, for physically realistic energy densities, the CTC's occur at distances from the axis greater than the radius of the visible universe by an immense factor. We then show that Mallett's solution has a curvature singularity on the axis, even in the case where the intensity of the light vanishes. Thus it is not the solution one would get by starting with Minkowski space and establishing a cylinder of light.

5 pages, RevTeX

Cited by in corpus (5)

• Energy conditions in general relativity and quantum field theory
• Formation of closed timelike curves in a composite vacuum/dust asymptotically-flat spacetime
• Frame dragging with optical vortices
• Axial symmetry cosmological constant vacuum solution of field equations with a curvature singularity, closed time-like curves and deviation of geodesics
• Geodesics in the static Mallett spacetime