Relativistic corrections to MOND from extended metric gravity theory with dimensionless scalar curvature
Clicks: 1
ID: 287258
2021
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This
article has not been analysed, so there is no overall score โ
reader engagement is measured and shown alongside.
Reader Engagement
0.0
/100
1 views
0 readers
AI Quality Assessment
Not analyzed
Readership in this journal
Ranked #3,523 of 3,757 articles by views in Malay Journal
Most read
Least read
Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 3,757 in total.
Mint this article as an NFT
Not yet mintedCreate a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.
5
SUSD
one-off · no wallet required
Abstract
This study derives the relativistic corrections to the MOND acceleration law by solving the ๐(ฯ) field equations proposed by Bernal et. al., with the choice ๐(ฯ)=ฯ^3/2, and where ฯ is a dimensionless scalar curvature. A metric ansatz involving a radial correction function ๐(๐) is constructed for a spherically symmetric, static spacetime. Non-relativistic MOND coincides with Newtonian gravity at a radial distance ๐=๐_๐=(๐บ๐/๐_0)^1/2 from the central mass ๐; this defines a transition radius between the two theories. Extending this to the relativistic case, the Schwarzschild solution is used as a boundary condition at this transition point. The field equations provide two first order differential equations of the correction function ฯ(๐). To first order in 1/๐, the two equations agree on a solution. At this level of approximation, the purely spatial components of the metric solution are equivalent to those of the Schwarzschild metric. The correction implies that the relativistic orbital speed of test bodies about a central mass is lower than the non-relativistic predictions; the correction vanishes for ๐โซ๐_๐. This study also derives the correction function for null geodesics in the MOND case; it shows that lensing and scattering effects are stronger than what general relativity predicts for ๐>๐_๐. To second order in 1/๐, the two differential equations of ฯ(๐) have different solutions; the theory does not provide any mechanism or criteria to identify which solution applies to a given situation. This anomalous dichotomy points to the possibility that either higher order approximations are required, or that there are extra assumptions that are currently beyond the theory at hand. Up to leading order, the metric solution in this study agrees with the perturbative solutions by Mendoza et. al., and Bernal et. al. Using variational techniques, this study derives the generalized field equations of metric ๐(ฯ) gravity; the variation involves a non-vanishing boundary term. This paper proves that a non-dynamical, Gibbons-Hawking-York type boundary counter-term similar to the one used in ๐(๐
) gravity can be used to construct a more complete action for this theory.
| Reference Key |
persistent_1760661057_68f18e4126b3d
Use this key to autocite in the manuscript while using
SciMatic Manuscript Manager or Thesis Manager
|
|---|---|
| Authors | Cruz, Donniel C. |
| Journal | Malay Journal |
| Year | 2021 |
| DOI |
DOI not found
|
| URL | |
| Keywords | Keywords not found |
Citations
No citations found. To add a citation, contact the admin at info@scimatic.org
Comments
No comments yet. Be the first to comment on this article.