Zero mass limit of Kerr spacetime is a wormhole

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

The zero mass limit of Kerr and Kerr-(anti) de Sitter space-times: revisited

“…Actually, the wave equation has two solutions. One of the solutions validates the Gibbons-Volkov result, with a singularity at the origin and along the z-axis, which is interpreted as a wormhole in [1]. The other solution is smooth at the origin, and at the z-axis.…”

“…This claim does not agree with contrary claims [3,4]. In an earlier paper [5], we gave one explicit solution for a scalar particle coupled to the zero mass of the limit of both the Kerr, Kerr-dS and Kerr-AdS space times, using the wave equation given by Gibbons and Volkov [1]. In that work we had confirmed the result of Gibbons and Volkov by explicitly obtaining one of the wave solutions, which has a cut singularity along the z-axis for the angular equation, and at the origin for the radial equation.…”

“…Both of the wave equations for u above seem to have a singularity at (u + 3 a 2 Λ ) = 0. We have to note that, for positive Λ, u should be more than − 3 a 2 Λ [1]. At u = − 3 a 2 Λ , we have the cosmological horizon.…”

“…As given in [1], if we take the time dependence as e iωt , and φ dependence as e −imφ , our wave equation for a scalar particle separates into two equations and read:…”

“…In a very interesting paper Gibbons and Volkov [1] have claimed that the mass going to zero limit of the Kerr [2] metric has wormhole solutions. This claim does not agree with contrary claims [3,4].…”