Non-Newtonian behavior in weak field general relativity for extended rotating sources

Abstract

Exact stationary axially symmetric solutions of the 4D Einstein equations with corotating pressureless perfect fluid sources are studied. A particular solution with approximately flat rotation curve is discussed in some detail. We find that simple Newtonian arguments overestimate the amount of matter needed to explain these curves by more than 30%. The crucial insight gained by this model is that the Newtonian approximation breaks down globally, even though it is valid locally everywhere. No conflict with solar system tests arises.

14 pp, 4 eps figures; v3: considerably extended version with added explanations and references, changed title, invited contribution to IJMPD

References in corpus (15)

• The universe seen at different scales
• EXPERIMENTAL LIMITS ON THE DARK MATTER HALO OF THE GALAXY FROM GRAVITATIONAL MICROLENSING.
• Cosmological Solutions in Macroscopic Gravity
• Information Entropy in Cosmology
• The York map as a Shanmugadhasan canonical transformation in tetrad gravity and the role of non-inertial frames in the geometrical view of the gravitational field
• The Chrono-geometrical Structure of Special and General Relativity: a Re-Visitation of Canonical Geometrodynamics
• Astrophysical Constraints on Modifying Gravity at Large Distances
• Can Galactic Observations Be Explained by a Relativistic Gravity Theory?
• General Relativity Resolves Galactic Rotation Without Exotic Dark Matter
• The need for dark matter in galaxies
• Comment on ``General Relativity Resolves Galactic Rotation Without Exotic Dark Matter'' by F.I. Cooperstock & S. Tieu
• Presence of exotic matter in the Cooperstock and Tieu galaxy model
• Just dust : About the (in)applicability of rotating dust solutions as realistic galaxy models
• Velocity Curves for Stars in Disk Galaxies: A case for Nearly Newtonian Dynamics
• Comments on "Perspectives on Galactic Dynamics via General Relativity"

Cited by in corpus (36)

• Cosmic clocks, cosmic variance and cosmic averages
• Conformally-flat, non-singular static metric in infinite derivative gravity
• Testing dark matter and geometry sustained circular velocities in the Milky Way with Gaia DR2
• Anisotropic Models for Globular Clusters, Galactic Bulges and Dark Halos
• Galactic dark matter effects from purely geometrical aspects of General Relativity
• Kinetic Theory of Collisionless Self-Gravitating Gases: II. Relativistic Corrections in Galactic Dynamics
• Towards a full general relativistic approach to galaxies
• Can General Relativity play a role in galactic dynamics?
• Dark matter, and its darkness
• On the rotation curve of disk galaxies in General Relativity
• Galactic Dynamics in General Relativity: the Role of Gravitomagnetism
• A method for evaluating models that use galaxy rotation curves to derive the density profiles
• A tale of analogies: gravitomagnetic effects, rotating sources, observers and all that
• Rigid rotation in GR and a generalization of the virial theorem
• Self-gravitating systems of ideal gases in the 1PN approximation
• Stationary rotating and axially symmetric dust systems as peculiar General Relativistic objects
• Reference frames in General Relativity and the galactic rotation curves
• Quasilocal Newtonian limit of general relativity and galactic dynamics
• Relativistic effects cannot explain galactic dynamics
• The Effect of Spacetime Curvature on Statistical Distributions
• Galactic Rotation Described with Thin-Disk Gravitational Model
• Distortions of Robertson-Walker metric in perturbative cosmology and interpretation as dark matter and cosmological constant
• Topological constraints on general relativistic galaxies: Exploring novel conical singularity networks
• Testing Refracted Gravity with kinematics of galaxy clusters
• On the low-energy limit of stationary and axisymmetric solutions in General Relativity
• Asymptotically Schwarzschild solutions in $f(R)$ extension of general relativity
• Galactic Rotation Described with Various Thin-Disk Gravitational Models
• The need for a nonlocal expansion in general relativity
• Fake dark matter from retarded distortions
• Non zero Coriolis field in Ehlers' Frame Theory
• Accretion of Galaxies around Supermassive Black Holes and a Theoretical Model of the Tully-Fisher and M-Sigma Relations
• Exploring Milky Way rotation curves with Gaia DR3: a comparison between $\Lambda$CDM, MOND, and General Relativistic approaches
• Quasilocal energy exchange and the null cone
• General Relativistic Thick Disks in the Accelerating Expanding Universe Dominated By Dark Energy
• Gravitational lensing observables in stationary and axisymmetric solutions in general relativity
• A simplified general relativistic model to analyze the structure of spiral galaxies