Spacetime-bridge solutions in vacuum gravity

TL;DR

This paper introduces novel vacuum solutions in gravity theory featuring bridge-like geometries connecting two asymptotically flat sheets, characterized by noninvertible tetrads and continuous invariant fields, unlike traditional Einstein vacuum solutions.

Contribution

It presents the first construction of spacetime-bridge solutions in vacuum gravity with noninvertible tetrads, expanding the landscape of possible vacuum geometries.

Findings

Solutions are classified into static and non-static types.

All invariant fields are continuous and finite across the bridge.

No analogues of these solutions exist in Einstein's vacuum gravity.

Abstract

Spacetimes, which are representations of a bridge-like geometry in gravity theory, are constructed as vacuum solutions to the first order equations of motion. Each such configuration consists of two copies of an asymptotically flat sheet, connected by a bridge of finite extension where tetrad is noninvertible. These solutions can be classified into static and non-static spacetimes. The associated SO(3,1) invariant fields, namely the metric, affine connection and field-strength tensor, are all continuous across the hypersurfaces connecting the invertible and noninvertible phases of tetrad and are finite everywhere. These regular spacetime-bridge solutions do not have any analogue in Einsteinian gravity in vacuum.