Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.08797 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917983911149568 |
|---|---|
| author | Re, Federico Piattella, Oliver F. |
| author_facet | Re, Federico Piattella, Oliver F. |
| contents | Ehlers' Frame Theory is a class of geometric theories parameterized by $λ:= 1/c^2$ and identical to the General Theory of Relativity for $λ\neq 0$. The limit $λ\to 0$ 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 $\boldsymbolω$, 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 $(η,H)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08797 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non zero Coriolis field in Ehlers' Frame Theory Re, Federico Piattella, Oliver F. General Relativity and Quantum Cosmology Astrophysics of Galaxies Ehlers' Frame Theory is a class of geometric theories parameterized by $λ:= 1/c^2$ and identical to the General Theory of Relativity for $λ\neq 0$. The limit $λ\to 0$ 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 $\boldsymbolω$, 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 $(η,H)$ 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. |
| title | Non zero Coriolis field in Ehlers' Frame Theory |
| topic | General Relativity and Quantum Cosmology Astrophysics of Galaxies |
| url | https://arxiv.org/abs/2504.08797 |