Geometry of Two-Sheeted Spacetime Solutions

TL;DR

This paper explores two-sheeted spacetime solutions in first order gravity, analyzing their geodesic structure, causal properties, and light deflection, revealing they resemble Schwarzschild exteriors from afar.

Contribution

It introduces and studies a class of double-sheeted vacuum solutions in first order gravity, highlighting their geometric and causal features.

Findings

Geodesic analysis reveals unique bridge-like causal structures.

Light deflection in these spacetimes mimics Schwarzschild predictions.

Solutions are indistinguishable from Schwarzschild at large distances.

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.