# Zero mass limit of Kerr spacetime is a wormhole

## TL;DR

This paper demonstrates that the zero mass limit of Kerr spacetime results in a non-trivial, locally flat wormhole with a singularity, challenging the common assumption that it reduces to flat Minkowski space.

## Contribution

It reveals that the zero mass Kerr spacetime is a wormhole with a negative tension ring, not flat space, and extends this interpretation to Kerr-(anti)-de Sitter spacetimes.

## Key findings

- Zero mass Kerr spacetime is a wormhole, not flat space.
- The limiting spacetime has two asymptotic regions and a curvature singularity.
- The interpretation extends to Kerr-(anti)-de Sitter spacetimes.

## Abstract

We show that, contrary to what is usually claimed in the literature, the zero mass limit of Kerr spacetime is not flat Minkowski space but a spacetime whose geometry is only locally flat. This limiting spacetime, as the Kerr spacetime itself, contains two asymptotic regions and hence cannot be topologically trivial. It also contains a curvature singularity, because the power-law singularity of the Weyl tensor vanishes in the limit but there remains a distributional contribution of the Ricci tensor. This spacetime can be interpreted as a wormhole sourced by a negative tension ring. We also extend the discussion to similarly interpret the zero mass limit of the Kerr-(anti)-de Sitter spacetime.