The hyperbolic Einstein-Rosen bridge

TL;DR

This paper explores the geometric structure of the hyperbolic Einstein-Rosen bridge, identifying three maximal extensions and analyzing its properties, including singularities and traversability by time-like curves.

Contribution

It introduces the hyperbolic Einstein-Rosen bridge as a new maximal extension with detailed geometric and causal properties.

Findings

Existence of three different maximal extensions of the Einstein-Rosen bridge.

The hyperbolic Einstein-Rosen bridge has a two-dimensional section diffeomorphic to a hyperboloid covering space.

The bridge includes a singularity satisfying cosmic censorship and is traversable by time-like curves.

Abstract

Using systematically isothermal coordinates we show that there exist three different maximal extensions of the original Einstein-Rosen bridge. One of them, the hyperbolic Einstein-Rosen bridge, has two-dimensional sections diffeomorphic to the covering space of an hyperboloid of revolution, a singularity satisfying the cosmic censorship and a bridge generated by light-like geodesics that can be traversed by time-like curves. The collapse process that might produce this object is an interesting open problem.