Non zero Coriolis field in Ehlers' Frame Theory

Abstract

Ehlers' Frame Theory is a class of geometric theories parameterized by $\lambda :=1/c^2$ and identical to the General Theory of Relativity for $\lambda \ne 0$. The limit $\lambda \to 0$ does not recover Newtonian gravity, as one might expect, but yields the so-called Newton-Cartan theory of gravity, which is characterized by a second gravitational field $\mathbf{\omega }$, called the Coriolis field. Such a field encodes at a non-relativistic level the dragging feature of general spacetimes, as we show explicitly for the case of the $(\eta ,H)$ geometries. Taking advantage of the Coriolis field, we apply Ehlers' theory to an axially symmetric distribution of matter, mimicking, for example, a disc galaxy, and show how its dynamics might reproduce a flattish rotation curve. In the same setting, we further exploit the formal simplicity of Ehlers' formalism in addressing non-stationary cases, which are remarkably difficult to be treated in the General Theory of Relativity. We show that the time derivative of the Coriolis field gives rise to a tangential acceleration which allows to study a possible formation in time of the rotation curve's flattish feature.

15 pages, no figures

References in corpus (22)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Classical Monopoles: Newton, NUT-space, gravomagnetic lensing and atomic spectra
• Gravito-electromagnetic analogies
• Review on Non-Relativistic Gravity
• Non-Newtonian behavior in weak field general relativity for extended rotating sources
• Testing dark matter and geometry sustained circular velocities in the Milky Way with Gaia DR2
• Gravitational Geons Revisited
• 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?
• Dark matter effects in vacuum spacetime
• On the rotation curve of disk galaxies in General Relativity
• Quasi-Maxwell interpretation of the spin-curvature coupling
• Pitfalls in applying gravitomagnetism to galactic rotation curve modelling
• The Coriolis field
• Discrete Matter, Far Fields, and Dark Matter
• General Relativity versus Dark Matter for rotating galaxies
• Reference frames in General Relativity and the galactic rotation curves
• General relativistic analogs of Poisson's equation and gravitational binding energy
• Editorial Note to: On the Newtonian Limit of Einstein's Theory of Gravitation (by Jürgen Ehlers)
• Relativistic effects cannot explain galactic dynamics
• Fake dark matter from retarded distortions

Cited by in corpus (1)

• Quasilocal Newtonian limit of general relativity and galactic dynamics