Topological constraints on general relativistic galaxies: Exploring novel conical singularity networks

TL;DR

This paper examines the topological features of van Stockum-Bonner spacetimes, revealing conical singularity networks that challenge their viability as models for relativistic galaxies and dark matter alternatives.

Contribution

It uncovers a network of conical singularities in these spacetimes, highlighting topological constraints that limit their use as realistic galaxy models.

Findings

Existence of quasi-regular singularity networks along the rotation axis.

Topological constraints restrict the physical viability of these spacetime models.

Implications for avoiding pathologies in relativistic galaxy modeling.

Abstract

The van Stockum-Bonner class of spacetimes can be interpreted as fully general relativistic models for rigidly rotating disc galaxies. Frame-dragging effects in these geometries demand a recalibration of the dark matter content relative to models based on Newtonian gravity. We investigate the previously overlooked topological structure of these spacetimes, in relation to the viability of fully general relativistic galaxy toy models. We discuss the appropriate boundary conditions for these solutions to model disc galaxies. For this class of spacetimes, we show the existence of a network of quasi-regular singularities along the rotation axis of the galaxies. The existence of such novel conical defect structures further restricts the physical viability of the van Stockum-Bonner class. Unwinding these issues is key to avoiding pathologies in future fully general relativistic modelling of alternative to dark matter.