Peculiarities for domain walls in Taub coordinates

Abstract

In the present letter the infinite domain wall geometry in GR (Vilenkin in Phys Rev D 23:852, 1981; Vilenkin in Phys Lett B 133:177, 1983; Ipser and Sikivie in Phys Rev D 30:712, 1984) is reconsidered in Taub coordinates (Taub in Ann Math 53:472, 1951). The use of these coordinates makes explicit that the regions between the horizons and the wall and the outer ones are flat. By use of these coordinates, it is suggested that points inside the horizon and outside never communicate each other. The wall is seen on the left and the right side as contracting and expanding portions of spheres and a plane singularity, which is the imprint the contracting and expanding domain wall. Particles of each region will never reach this imprint. In addition, at some point during the evolution of the system, four curious holes inside the space time appear, growing at the speed of light. This region is not parameterized by the standard Taub coordinates, and the boundary of this hole adsorbs all the particles that intersect it. The boundary of these holes are composed by points which in the coordinates of [1–3] are asymptotic, in the sense that they correspond to trajectories tending to infinite values of the time or space like coordinates, while the proper time elapsed for the travel is in fact finite. This is not paradoxical, as the coordinates [1–3] are not to be identified with the true lengths or proper time on the space time. The correct interpretation of the boundary is particularity relevant when studying scattering of quantum fields approaching the domain wall. A partial analysis about this issue is done in the last section.