A Simple Model for Explaining Galaxy Rotation Curves

Wojnar, Aneta; Sporea, Ciprian A.; Borowiec, A.

doi:10.3390/galaxies6030070

Cited by 13 publications

(13 citation statements)

References 81 publications

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“…It is unlikely, a priori, that all fits are possible for other galaxies, but that for these statistical reasons, this is possible for the vast majority of them. Note that recent results [14] using the Formula (34) in a purely phenomenological way and without any theoretical justifications allowed the good fits of 18 additional galaxies.…”

Section: Discussionmentioning

confidence: 94%

“…In this, we tried to follow as much as possible the historical approach of the American and Dutch mathematics schools which historically mathematically conceptualized projective differential geometry and its application to relativity. To quote Wojnar et al [14], we obtain a much simpler and in our opinion more mathematically justified modification of Newton's law.…”

Section: Introductionmentioning

confidence: 89%

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Applications of a Particular Four-Dimensional Projective Geometry to Galactic Dynamics

Rubin

2018

Galaxies

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Relativistic localizing systems that extend relativistic positioning systems show that pseudo-Riemannian space-time geometry is somehow encompassed in a particular four-dimensional projective geometry. The resulting geometric structure is then that of a generalized Cartan space (also called Cartan connection space) with projective connection. The result is that locally non-linear actions of projective groups via homographies systematically induce the existence of a particular space-time foliation independent of any space-time dynamics or solutions of Einstein’s equations for example. In this article, we present the consequences of these projective group actions and this foliation. In particular, it is shown that the particular geometric structure due to this foliation is similar from a certain point of view to that of a black hole but not necessarily based on the existence of singularities. We also present a modified Newton’s laws invariant with respect to the homographic transformations induced by this projective geometry. Consequences on galactic dynamics are discussed and fits of galactic rotational velocity curves based on these modifications which are independent of any Modified Newtonian Dynamics (MOND) or dark matter theories are presented.

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Section: Discussionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 89%

Applications of a Particular Four-Dimensional Projective Geometry to Galactic Dynamics

Rubin

2018

Galaxies

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“…The anomalous rotation curves of the galaxies have been invoked as a convincing proof of the existence of a new kind of matter that not couples to electromagnetic radiation and, consequently, is called dark matter. Anyway, many authors propose that a modified theory of gravity may account for these anomalies without invoking any kind of dark matter [51][52][53][54][55]. For all these reasons, it is not far-fetched to believe that General Relativity could be an incomplete theory, and not only in the sense that it remains inconsistent with quantum theory, but even from a purely classical point of view.…”

Section: Discussionmentioning

confidence: 99%

Angular Momentum and Energy Transfer in a Whitehead's Theory of Gravity

Acedo¹

2018

Preprint

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In this paper, we revisit a modified version of the classical Whitehead's theory of gravity in which all possible bilinear forms are considered to define the corresponding metric. Although, this is a linear theory that fails to give accurate results for the most sophisticated predictions of general relativity, such as gravity waves, it can still provide a convenient framework to analyze some new phenomena in the Solar System. In particular, recent development in the accurate tracking of spacecraft and the ephemerides of planetary positions have revealed certain anomalies in relation with our standard paradigm for celestial mechanics. Among them the so-called flyby anomaly and the anomalous increase of the astronomical unit play a prominent role. In the first case the total energy of the spacecraft changes during the flyby and a secular variation of the semi-major axis of the planetary orbits is found in the second anomaly. For this to happen it seems that a net energy and angular momentum transfer is taken place among the orbiting and the central body. We evaluate the total transfer per revolution for a planet orbiting the Sun in order to predict the astronomical unit anomaly in the context of Whitehead's theory. This could lead to a more deeply founded hypothesis for an extended gravity model.

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“…More confusingly, with the existing surveys, people had been more interested in declines in the curves associated with mass distribution cut-offs, so even when data already exhibit early signs of rising tails, they are instead interpreted as "asymptotically approaching a flat curve after a temporary dip" (see many examples of this morphology in the agnostic sample of THINGS curves in Wojnar et al [47]) and used to argue that earlier results showing declining curves do not provide the full picture, and making observations further out instead produces once again "flat" profiles. We do not quite agree with this "dip" interpretation (which assumes that the curves will flatten off rather than keep rising), because to produce this "rising back up" feature on top of the CDM or MOND profiles (which are smoothly declining or flat at large distances), baryonic matter must form a high density shell at extremely large galactocentric distances, and we have not seen any discussions as to why and how such a shell should form (especially since this morphology occurs quite frequently, the shell must be a ubiquitous robust feature of galaxies), or indeed seen any observational evidence for the existence of such shells at all.…”

Section: Anatomy Of Rotation Curvesmentioning

confidence: 99%

Modeling the Rising Tails of Galaxy Rotation Curves

Zhang

2019

Galaxies

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It is well known, but under-appreciated in astrophysical applications, that it is possible for gravity to take on a life of its own in the form of Weyl-curvature-only metrics (note that we are referring to the Weyl-only solutions of ordinary General Relativity; we are not considering Weyl conformal gravity or any other modified gravity theories), as numerous examples demonstrate the existence of gravitational fields not being sourced by any matter. In the weak field limit, such autonomous gravitational contents of our universe manifest as solutions to the homogeneous Poisson's equation. In this note, we tentatively explore the possibility that they may perhaps account for some phenomenologies commonly attributed to dark matter. Specifically, we show that a very simple solution of this kind exists that can be utilized to describe the rising tails seen in many galaxy rotation curves, which had been difficult to reconcile within the cold dark matter or modified Newtonian dynamics frameworks. This solution may also help explain the universal ∼1 Gyr rotation periods of galaxies in the local universe.

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A Simple Model for Explaining Galaxy Rotation Curves

Abstract: A new simple expression for the circular velocity of spiral galaxies is proposed and tested against HI Nearby Galaxy Survey (THINGS) data set. Its accuracy is compared with the one coming from MOND.

Cited by 13 publications

References 81 publications

Applications of a Particular Four-Dimensional Projective Geometry to Galactic Dynamics

Applications of a Particular Four-Dimensional Projective Geometry to Galactic Dynamics

Angular Momentum and Energy Transfer in a Whitehead's Theory of Gravity

Modeling the Rising Tails of Galaxy Rotation Curves

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