Zero Mass limit of Kerr-MOG Black Hole Equals Wormhole

TL;DR

This work shows that the zero-mass limit of the Kerr-MOG black hole is a locally flat wormhole with a ring-like conical singularity, obtained via a Kerr-Schild decomposition within Modified Gravity. By deriving the Kerr-MOG Kerr-Schild form and analyzing two-patch coverings, the authors demonstrate a topologically nontrivial spacetime with two asymptotic regions connected through a throat, persisting despite local flatness as ${\

Abstract

It has been argued in existing literature that the zero mass limit of Kerr spacetime corresponds to either flat Minkowski spacetime or a wormhole exhibiting a locally flat geometry. In this study, we examine that the zero mass limit of the Kerr-MOG black hole is equivalent to a wormhole. Moreover, we derive the Kerr-Schild form of the Kerr-MOG black hole through specific coordinate transformations. We further investigate the physical and topological characteristics of the Kerr-MOG black hole within the framework of modified gravity. Our analysis also includes a discussion of the wormhole using cylindrical coordinates, which comprises two distinct coordinate patches. Furthermore, we extend our analysis to the Kerr-Newman black hole and show that the \emph{zero mass limit of the Kerr-Newman black hole does not yield a wormhole}. However, if we impose an additional criterion such that \emph{both the mass parameter and the charge parameters are equal to zero}, then the Kerr-Newman black hole will be a wormhole.