In a paper by Ken Olum and Allen Everett, the authors claimed to have found problems with Mallett's analysis. One of their objections is that the spacetime which Mallett used in his analysis contains a singularity even when the power to the laser is off, which would not be expected to arise naturally if the circulating laser were activated in previously empty space. Mallett has not offered a published response to Olum and Everett, but in his book Time Traveler, he mentions that he was unable to directly model the optical fiber or photonic crystal which bends the light's path as it travels through it, so the light circulates around rather than moving in a straight line; as a substitute, he chose to include a "line source" (a type of one-dimensional singularity) which would act as a "geometric constraint", bending spacetime in such a way that the light would circulate around on a helix -shaped path in vacuum (for an older solution involving an infinite cylinder which creates CTCs, in this case due to the cylinder's own rotation rather than light circulating around it, see the Tipler cylinder). He notes that closed timelike curves are present in a spacetime containing both the line source and the circulating light, while they are not present in a spacetime containing only the line source, so that "the closed loops in time had been produced by the circulating flow of light, and not by the non-moving line source." However, he does not provide any additional argument as to why we should expect to see closed timelike curves in a different spacetime where there is no line source, and where the light is caused to circulate due to passing through a physical substance like a photonic crystal rather than circulating in vacuum due to the curved spacetime around the line source.