A mathematical analysis reports that a family of theoretical black-hole spacetimes can be continued through a surface where the radial coordinate approaches infinity. The study focuses on the global structure of an exact theoretical solution, including the region beyond that surface.
The study examines Kerr-Newman-Bertotti-Robinson spacetime, along with its Schwarzschild-BR subcase. These are analytical models rather than objects drawn from an observational sample. To show the global arrangement, the paper constructs horizon-penetrating coordinates and a Carter-Penrose diagram.
The central construction replaces the radial coordinate with its reciprocal, meaning one divided by the original radial value. In that coordinate, the paper reports that the whole family can be extended continuously as the radial coordinate approaches infinity. The extension joins a patch at positive radial values to one at negative radial values.
The route through the geometry matters
The continuation is not the same in every direction. The conformal structure, meaning the way the spacetime's boundaries and infinite regions fit together, varies with rotation and with the fixed polar direction chosen for the analysis.
In the Schwarzschild-BR case, directions away from the poles can be joined into what the paper describes as a geodesically maximal manifold, a spacetime in which the paths under study continue as far as the geometry allows. The proposed construction carries those routes to singularities where the radial coordinate is zero. Polar routes behave differently and end at a conformal boundary, a mathematical edge at infinity.
In the rotating Kerr-Newman-BR geometry, the physical singularity is a ring at zero radial coordinate and at the equatorial polar angle. The paper consequently distinguishes among equatorial, polar and intermediate directions when describing the extension.
For a generic polar route, an observer moving toward increasing radial coordinate crosses the inner and outer horizons and then reaches what the paper calls proper conformal infinity. The paper uses horizon-penetrating coordinates to represent these passages in a Carter-Penrose diagram.
Along the equatorial plane, an observer crosses both horizons and passes through the surface where the radial coordinate approaches positive infinity. The observer then reaches the singularity from the negative-radial side.
An infinite chain, with a warning
For directions that are neither equatorial nor polar, the proposed extension produces a manifold with no singularity or conformal infinity along the described route. The author represents it as an infinite combination of parallel black-hole spacetimes linked by a throat at positive radial infinity, giving the construction a wormhole-like character.
In the extremal Kerr-Newman-BR case, the paper reports one horizon while the other reported global properties remain unchanged. The directional differences and the proposed continuation therefore still organize the picture.
The author presents the resulting constructions as geodesically maximal manifolds and says the formal gluing introduces no matter content at the joining surface. But the paper does not establish that this is the only continuous extension. It explicitly notes that other continuous extensions may exist.
That caveat is important because the parallel-universe outcome belongs to the proposed gluing, not to every possible extension of the spacetime. The paper leaves open whether a different continuous construction could produce a different global picture.
A mathematical result, not an observation
The supplied record identifies the work as an arXiv preprint, version 1. It is a theoretical study of the global structure of Kerr-Newman-BR spacetime and related subcases.
The work was supported by the Czech Science Foundation through grant GACR 26-22381S and by Charles University through grant GAUK 260325. The paper states that data supporting its findings are openly available at reference [26].
Paper data and sources
Original title: Global structure of Kerr-Newman-BR spacetime
Authors: Hryhorii Ovcharenko
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text