Reference frames in General Relativity and the galactic rotation curves
arXiv:2303.17516 · doi:10.1103/PhysRevD.108.044056
Abstract
The physical interpretation of the exact solutions of the Einstein field equations is, in general, a challenging task, part of the difficulties lying in the significance of the coordinate system. We discuss the extension of the International Astronomical Union (IAU) reference system to the exact theory. It is seen that such an extension, retaining some of its crucial properties, can be achieved in a special class of spacetimes, admitting nonshearing congruences of observers which, at infinity, have zero vorticity and acceleration. As applications, we consider the Friedmann-Lemaître-Robertson-Walker (FLRW), Kerr and Newman-Unti-Tamburino (NUT) spacetimes, the van Stockum rotating dust cylinder, spinning cosmic strings and, finally, we debunk the so-called Balasin-Grumiller (BG) model, and the claims that the galaxies' rotation curves can be explained through gravitomagnetic effects without the need for dark matter. The BG spacetime is shown to be completely inappropriate as a galactic model: its dust is actually static with respect to the asymptotic inertial frame, its gravitomagnetic effects arise from unphysical singularities along the axis (a pair of NUT rods, combined with a spinning cosmic string), and the rotation curves obtained are merely down to an invalid choice of reference frame -- the congruence of zero angular momentum observers, which are being dragged by the singularities.
30 pages, 10 figures. Slightly improved Section III.D, typos corrected, references added. Supplemental material is provided in the ancillary Mathematica files "NUTmetrics.nb" and "BGmetric.nb". Matches the final version published in PRD as an Editor's Suggestion
References in corpus (49)
- Cosmic strings
- The basics of gravitational wave theory
- Cosmic String Interpretation of NANOGrav Pulsar Timing Data
- Probing the gravitational wave background from cosmic strings with LISA
- Black Saturn
- The Many Faces of Gravitoelectromagnetism
- Classical Monopoles: Newton, NUT-space, gravomagnetic lensing and atomic spectra
- The fundamental definition of 'radial velocity'
- Interpreting the C-metric
- The intrinsic derivative and centrifugal forces in general relativity: I. Theoretical foundations
- Gravito-electromagnetic analogies
- The Gaia reference frame for bright sources examined using VLBI observations of radio stars
- Non-Newtonian behavior in weak field general relativity for extended rotating sources
- Cylindrical Systems in General Relativity
- Bobbing and Kicks in Electromagnetism and Gravity
- Theorems on shear-free perfect fluids with their Newtonian analogues
- Ability of LISA to detect a gravitational-wave background of cosmological origin: the cosmic string case
- Testing dark matter and geometry sustained circular velocities in the Milky Way with Gaia DR2
- Spacetime dynamics of spinning particles - exact electromagnetic analogies
- Gravitomagnetism and Relative Observer Clock Effects
- Intrinsic definitions of "relative velocity" in general relativity
- On the parameters of Lewis metric for the Weyl class
- Stationary and static cylindrically symmetric Einstein spaces of the Lewis form
- Galactic dark matter effects from purely geometrical aspects of General Relativity
- Post-Newtonian Approximation in Maxwell-Like Form
- Simultaneity and generalized connections in general relativity
- Shear free solutions in General Relativity Theory
- Can General Relativity play a role in galactic dynamics?
- Kerr metric, static observers and Fermi coordinates
- On the rotation curve of disk galaxies in General Relativity
- General relativistic dynamics applied to the rotation curves of galaxies
- Viable Gauge Choices in Cosmologies with Non-Linear Structures
- Galactic Dynamics in General Relativity: the Role of Gravitomagnetism
- Sagnac Effect, Ring Lasers and Terrestrial Tests of Gravity
- Quasi-Maxwell interpretation of the spin-curvature coupling
- Cylindrical analogue of NUT space: spacetime of a line gravomagnetic monopole
- Cosmological perturbations: a new gauge-invariant approach
- Global aspects of gravitomagnetism
- Rigid rotation in GR and a generalization of the virial theorem
- Gravitational Magnus effect
- Pitfalls in applying gravitomagnetism to galactic rotation curve modelling
- Relativistic Reference Frames for Astrometry and Navigation in the Solar System
- Gaussian Curvature and Global effects : gravitational Aharonov-Bohm effect revisited
- Gravitomagnetism in the Lewis cylindrical metrics
- General relativistic analogs of Poisson's equation and gravitational binding energy
- Expanding perfect fluid generalizations of the C-metric
- The Gravito-Electromagnetic Approximation to the Gravimagnetic Dipole and its Velocity Rotation Curve
- A geometric method to determine the direction of electric field due to a uniformly charged line segment
- Shear-free perfect fluids with a barotropic equation of state in general relativity: the present status
Cited by in corpus (5)
- Pitfalls in applying gravitomagnetism to galactic rotation curve modelling
- Stationary rotating and axially symmetric dust systems as peculiar General Relativistic objects
- Relativistic effects cannot explain galactic dynamics
- Topological constraints on general relativistic galaxies: Exploring novel conical singularity networks
- Non zero Coriolis field in Ehlers' Frame Theory