General Relativistic Fall on a Thick-Plate

TL;DR

This paper models a thick-plate in a Kasner-type spacetime to analyze gravitational fall, revealing conditions for Newtonian-like acceleration and unbounded escape velocity, extending thin-shell domain wall concepts.

Contribution

It introduces an exact thick-plate model using Kasner-type spacetime, extending thin-shell domain wall analysis to a more realistic thick-structure with detailed geodesic and gravitational properties.

Findings

Conditions for Newtonian-like fall with constant negative acceleration.

Escape velocity of the thick-shell is unbounded.

Metric is regular, but energy-momentum remains problematic.

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 with symmetry axis $z$ and thickness $0\leq z\leq z_{0}$ are investigated. Geodesic analysis determines the possibility of a Newtonian-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.