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

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.

13 pages, 1 figure

References in corpus (21)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• The Confrontation between General Relativity and Experiment
• Dark Halos of M31 and the Milky Way
• Mapping the Milky Way Disk with Gaia DR3: 3D extended kinematic maps and rotation curve to $\approx 30$ kpc
• Non-Newtonian behavior in weak field general relativity for extended rotating sources
• General relativistic velocity: the alternative to dark matter
• Galactic dark matter effects from purely geometrical aspects of General Relativity
• Towards a full general relativistic approach to galaxies
• Can General Relativity play a role in galactic dynamics?
• On the rotation curve of disk galaxies in General Relativity
• Galactic Dynamics in General Relativity: the Role of Gravitomagnetism
• A tale of analogies: gravitomagnetic effects, rotating sources, observers and all that
• Rigid rotation in GR and a generalization of the virial theorem
• Pitfalls in applying gravitomagnetism to galactic rotation curve modelling
• Stationary rotating and axially symmetric dust systems as peculiar General Relativistic objects
• Reference frames in General Relativity and the galactic rotation curves
• Relativistic effects cannot explain galactic dynamics
• Effective galactic dark matter: first order general relativistic corrections
• Re-weighting dark matter in disc galaxies: a new general relativistic observational test
• Equatorial Lensing in the Balasin-Grumiller Galaxy Model
• Exact solutions for differentially rotating galaxies in general relativity