General Relativistic Fall on a Thick-Plate

Abstract

As an extension of a thin-shell, we adopt a single parametric plane-symmetric Kasner-type spacetime to represent an exact thick plate. This naturally extends the domain wall spacetime to a domain thick-wall case. Physical properties of such a plate (or an infinite slab) with symmetry axis z and thickness 0 <= z <= z(0) are investigated. Geodesic analysis determines the possibility of aNewtonian-like fall, namely with constant negative acceleration as it is near the Earth's surface. This restricts the Kasner-like exponents to a finely-tuned set, which together with the thickness and energy parameter determine the G-force of the plate. In contrast to the inverse square law, the escape velocity of the thick shell is unbounded. The metric is regular everywhere but expectedly the energy-momentum of the thick plate remains problematic.