Spacetime contraction in the Einstein's elevator

Abstract

The equivalence principle was explained by Einstein using the didactic "mental experiment" of a uniform gravitational field inside an elevator. The Earth gravitational field is not really uniform so the question about how to create a uniform gravitational field is legitimate. To this aim, instead of using metrics depending on spatial coordinates, we have studied a cosmological-like metric and we have found that, under suitable assumptions, it is possible to measure a uniformly accelerated motion for the test particles moving inside the elevator.