Geometry of Two-Sheeted Spacetime Solutions

Abstract

In contrast to Einstein's theory, the first order formulation of gravity turns out to be a natural habitat for double-sheeted spacetime solutions which satisfy the vacuum field equations everywhere. These bridge-like geometries exhibit degenerate tetrads at their core that separates the two sheets. Here we study the geodesics of these solutions and elucidate their causal structure. These spacetimes emerge as a classical realization of a two-universe solution in pure gravity. We also find the angle of deflection of light propagating in a bridge geometry. From this, we conclude that this spacetime would be indistinguishable from the Schwarzschild exterior when observed from asymptotia.