- #1

kodama

- 1,026

- 139

- TL;DR Summary
- weak field limit of GR

for over a century the weak field limit of general relativity is Newtonian, which when applied to galaxy rotation curves requires cold dark matter as Newtonian limit is too weak

this recent paper

[Submitted on 1 Aug 2024]

Marco Galoppo, David L. Wiltshire, Federico Re

the conclusion of the paper

specifically standard calculations should also include

factoring this, and applying it to galaxies,

in our solar system, the weak field limit of general relativity is Newtonian, but on the scale of galaxies, "axisymmetric gravitationally bound differentially rotating matter distributions with internal pressure. The self-consistent coupling of quasilocal gravitational energy and angular momentum" factor in the equation of general relativity giving rise to MOND.

so if there is any physicist here with expertise in general relativity and astrophysics, does self-consistent coupling of quasilocal gravitational energy and angular momentum leads to a modified Poisson equation leading to MOND rather than Newton in the weak field limit of general relativity when applied to galaxies? is this paper plausible?

prior calculations of general relativity didn't account for gravitational energy and angular momentum on the scale of galaxies

this recent paper

**arXiv:2408.00358**(gr-qc)[Submitted on 1 Aug 2024]

### Quasilocal Newtonian limit of general relativity and galactic dynamics

Marco Galoppo, David L. Wiltshire, Federico Re

A new Newtonian limit of general relativity is established for stationary axisymmetric gravitationally bound differentially rotating matter distributions with internal pressure. The self-consistent coupling of quasilocal gravitational energy and angular momentum leads to a modified Poisson equation. The coupled equations of motion of the effective fluid elements are also modified, with quasilocal angular momentum and frame-dragging leading to novel dynamics. The solutions of the full system reproduce the phenonomenology of collisionless dark matter for disc galaxies, offering an explanation for their observed rotation curves. Halos of abundant cold dark matter particles are not required.

Comments: 6 pages, 2 figures

Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); Astrophysics of Galaxies (astro-ph.GA); High Energy Physics - Phenomenology (hep-ph)

Cite as: arXiv:2408.00358 [gr-qc]

(or arXiv:2408.00358v1 [gr-qc] for this version)

https://doi.org/10.48550/arXiv.2408.00358

### Marco Galoppo

###

### University of Canterbury | UC · Department of Physics and Astronomy

### David Wiltshire is a Professor of Physics at the University of Canterbury, Christchurch, New Zealand. He is known for his work in higher-dimensional gravity, brane worlds, black holes and cosmology.

the conclusion of the paper

The authors conclude:

‘This discovery has far-reaching consequences … Comparisons with MOND phenomenology potentially open the prospect not only ofplacing MOND within the theoretical framework of general relativity, but also of providing insights into the development of this important new physical limit of Einstein’s theory.’

specifically standard calculations should also include

axisymmetric gravitationally bound differentially rotating matter distributions with internal pressure. The self-consistent coupling of quasilocal gravitational energy and angular momentum leads to a modified Poisson equation.

factoring this, and applying it to galaxies,

*general relativity*, weak field limit gives MOND rather than Newton, obviating the need for cold dark matter.in our solar system, the weak field limit of general relativity is Newtonian, but on the scale of galaxies, "axisymmetric gravitationally bound differentially rotating matter distributions with internal pressure. The self-consistent coupling of quasilocal gravitational energy and angular momentum" factor in the equation of general relativity giving rise to MOND.

so if there is any physicist here with expertise in general relativity and astrophysics, does self-consistent coupling of quasilocal gravitational energy and angular momentum leads to a modified Poisson equation leading to MOND rather than Newton in the weak field limit of general relativity when applied to galaxies? is this paper plausible?

prior calculations of general relativity didn't account for gravitational energy and angular momentum on the scale of galaxies