Effects of Higher Order Retarded Gravity

In a recent paper, we have a shown that the flattening of galactic rotation curves can be explained by retardation. However, this will rely on a temporal change of galactic mass. In our previous work, we kept only second order terms of the retardation time in our analysis, while higher terms in the Taylor expansion where not considered. Here we consider analysis to all orders and show that a second order analysis will indeed suffice, and higher order terms can be neglected.

Effects of Higher Order Retarded Gravity

In a recent paper we have a shown that the flattening of galactic rotation curves can be explained by retardation. However, this will rely on a temporal change of galactic mass. In our previous work we have kept only second order terms of the retardation time in our analysis, while higher terms in the Taylor expansion where not considered. Here we consider analysis to all orders and show that indeed a second order analysis will suffice, and higher order terms can be neglected.

On planetary orbits in entropic gravity

Starting with an entropy that includes volumetric, area and length terms as well as logarithmic contributions, we derive the corresponding modified Newtonian gravity and derive the expression for planetary orbits. We calculate the shift of the perihelion of Mercury to find bounds to the parameters associated to the modified Newtonian gravity. We compare the parameter associated to the volumetric contribution in the entropy-area relationship with the value derived for galactic rotation curves and the value obtained from the cosmological constant.

On the Three Laws of Rotationally Supported Galaxies: The Observed Flattening of Rotation Curves, the Baryonic Tully-Fischer Relation and the Mass Discrepancy-acceleration Relation

In this paper we will find that, according to holographic principle {\cite{Holografico}} and thus considering Universe as the ensemble of $\aleph$ information bits or minimum particles of mass $m_{g}$, the contribution to galactic rotation curves can be due the rest of the visible Universe through a non-local collective gravitational interaction of all particles within the Universe's horizon, as a consequence of which all particles are gravitationally entangled and form a unified statistical ensemble. Therefore, we can to describe this global effect in terms of standard local Newtonian gravity within galaxies for the explanation of flatness galactic rotation curves as a possible alternative to the dark matter or MOND hypothesis. We will find a solution for the baryonic Tully-Fischer relation: $M_{b} = A v_{f}^4 \iff A = \left[a_{0}G \right]^{-1}$ with $a_{0} = \frac{cH_{0}}{2\pi}$, where $H_{0}$ is the Hubble constant at present Time $t_{0}$ and $M_{b}$, $G$ and $c$ are the galaxy baryonic mass, gravitational constant and constant speed of light in vacuum respectively. Also we will find the mass discrepancy-acceleration relation, thus obtaining a possible solution for each of the three laws of rotationally supported galaxies proposed in ({\cite{McGaugh}},{\cite{McGaugh1}}).

Testing Bose–Einstein condensate dark matter models with the SPARC galactic rotation curves data

The nature of one of the fundamental components of the Universe, dark matter, is still unknown. One interesting possibility is that dark matter could exist in the form of a self-interacting Bose–Einstein Condensate (BEC). The fundamental properties of dark matter in this model are determined by two parameters only, the mass and the scattering length of the particle. In the present study we investigate the properties of the galactic rotation curves in the BEC dark matter model, with quadratic self-interaction, by using 173 galaxies from the recently published Spitzer Photomery & Accurate Rotation Curves (SPARC) data. We fit the theoretical predictions of the rotation curves in the slowly rotating BEC models with the SPARC data by using genetic algorithms. We provide an extensive set of figures of the rotation curves, and we obtain estimates of the relevant astrophysical parameters of the BEC dark matter halos (central density, angular velocity and static radius). The density profiles of the dark matter distribution are also obtained. It turns out that the BEC model gives a good description of the SPARC data. The presence of the condensate dark matter could also provide a solution for the core–cusp problem.

Debated Models for Galactic Rotation Curves: A Review and Mathematical Assessment

Proposed explanations of galactic rotation curves (RC = tangential velocity vs. equatorial radius, determined from Doppler measurements) involve dramatically different assumptions. A dominant, original camp invoked huge amounts of unknown, non-baryonic dark matter (NBDM) in surrounding haloes to reconcile RC simulated using their Newtonian orbital models (NOMs) for billions of stars in spiral galaxies with the familiar Keplerian orbital patterns of the few, tiny planets in our Solar System. A competing minority proposed that hypothetical, non-relativistic, non-Newtonian forces govern the internal motions of galaxies. More than 40 years of controversy has followed. Other smaller groups, unsatisfied by explanations rooted in unknown matter or undocumented forces, have variously employed force summations, spin models, or relativistic adaptations to explain galactic rotation curves. Some small groups have pursued inverse models and found no need for NBDM. The successes, failures, and underlying assumptions of the above models are reviewed in this paper, focusing on their mathematical underpinnings. We also show that extractions of RC from Doppler measurements need revising to account for the effect of galaxy shape on flux-velocity profiles and for the possible presence of a secondary spin axis. The latter is indicated by complex Doppler shift patterns. Our findings, combined with independent evidence such as hadron collider experiments failing to produce non-baryonic matter, suggest that a paradigm shift is unfolding.