General Relativity and the Tully-Fisher Relation for Rotating Galaxies

The flat limit of rotational velocity (vφ) approximately equal to the “edge”-velocity of a galaxy is related to the baryonic mass (MB) via the T-F relationship with n ≈ 4. We explore the connection between mass and the limiting velocity in the framework of general relativity (GR) using the Weyl metric for axially-symmetric galaxies that are supported entirely by their rotational motion. While for small distances from the center, the Newtonian description is accurate as one moves beyond the (baryonic) edge of the galaxy, Lenz’s law and non-linearity of the gravitational field inherent in GR not only lead to a flat velocity (obviating its Keplerian fall), but also provide its tight log-log relationship with the enclosed (baryonic) mass.

Multi-Barycenter Mechanics, N-Body Problem and Rotation of Galaxies and Stars

In the present paper, the establishment of a systematic multi-barycenter mechanics is based on the multi-particle mechanics. The new theory perfects the basic theoretical system of classical mechanics, which finds the law of mutual interaction between particle groups, reveals the limitations of Newton’s third law, discovers the principle of the intrinsic relationship between gravity and tidal force, reasonably interprets the origin and change laws for the rotation angular momentum of galaxies and stars and so on. By applying new theory, the multi-body problem can be transformed into a special two-body problem and for which an approximate solution method is proposed, the motion law of each particle can be roughly obtained.

The Origin, Properties and Detection of Dark Matter and Dark Energy

The pictures from the James Webb Space Telescope (JWST) suggest that massive galaxies were already at the beginning of the expansion of the Universe because there was too short time to create them. It is consistent with the new cosmology presented within the Scale-Symmetric Theory (SST). The phase transitions of the initial inflation field described in SST lead to the Protoworld—its core was built of dark matter (DM). We show that the DAMA/LIBRA annual-modulation amplitude forced by the change of the Earth’s velocity (i.e. baryonic-matter (BM) velocity) in relation to the spinning DM field in our Galaxy’s halo should be very low. We calculated that in the DM-BM weak interactions are created single and entangled spacetime condensates with a lowest mass/energy of 0.807 keV—as the Higgs boson they can decay to two photons, so we can indirectly detect DM. Our results are consistent with the averaged DAMA/LIBRA/COSINE-100 curve describing the dependence of the event rate on the photon energy in single-hit events. We calculated the mean dark-matter-halo (DMH) mass around quasars, we also described the origin of the plateaux in the rotation curves for the massive spiral galaxies, the role of DM-loops in magnetars, the origin of CMB, the AGN-jet and galactic-halo production, and properties of dark energy (DE).

Theory to the Mystery of the Super Massive Black Holes

Vera Rubin measured the rotational speeds of galaxies, Ref. [1] 1983, and she found that the masses of galaxies were not enough to produce the measured speeds of rotation. Therefore, it was inferred that there must be an unknown matter which is many times the known visible and dark matter. In this study, the solution to the dark matter mystery of spiral galaxies is a four-dimensional mass in the space of four distance dimensions, coordinates: x,y,z,x', in which x' is the fourth distance dimension. The four-dimensional mass is a black hole, and it generates the main gravitation field of the galaxy. This mysterious black hole is located in the fourth dimension at the distance x' = X'. The rotational speed distribution curves of the galaxy NGC 3198 have been presented in Ref. [2]. The speed distribution curve of the galactic halo in that publication corresponds to the speed distribution curve of the four-dimensional black hole in this study. In order to find out how well this four-dimensional model functions, the speed distribution curve of the four-dimensional black hole was calculated, and it was compared with the halo curve of Ref. [2]. The conclusion was that the calculated speed distribution curve of the black hole was a good match to the halo curve of Ref. [2]. Furthermore, the rotational speed distribution curves of the four-dimensional black hole were calculated by using different values of the reduced distance X', which yielded at the distance X' = 0 a black hole of radius R = 7.7 × 1017 m. By using the relativistic Lorentz transformation, it was shown in this study that a star falling into the four-dimensional black hole remains rotating it at near speed of light, and cannot fall into the actual black hole.

The Principle of Equivalence: Periastron Precession, Light Deflection, Binary Star Decay, Graviton Temperature, Dark Matter, Dark Energy and Galaxy Rotation Curves

The nature of the principle of equivalence is explored. The path of gravitons is analyzed in an accelerating system equivalent to a gravitating system. The finite speed of the graviton results in a delay of the gravitational interaction with a particle mass. From the aberration found in the path of the graviton we derive the standard expression for the advancement of the periastron of the orbit of the mass around a star. In a similar way, by analysing the aberrations of the graviton and light paths in an accelerating reference frame, the expression for the deflection of light by a massive body is obtained identically to the standard result. We also examine the binary star system and calculate the decay in its orbital period. The decay is attributed to the redshift of the graviton frequency relative to the accelerating system. Here too, we obtain good agreement with experimental measurements. Also, hypothesizing that gravitons behave like photons, we determine the temperature of the gravitons in a binary star system and form the Bose-Einstein distribution. Finally, we show how the redshift of gravitons may be the source of dark matter, dark energy and flat line spiral galaxy rotation curves.

Galaxy Rotation in the Space of Four Distance Dimensions

This study contains the solution of the dark matter mystery of spiral galaxies by using the space of four distance dimensions x, y, z, x', in which x' is the fourth distance dimension. The calculation of galaxy rotation has been presented in the space of four dimensions by using two dimensional section x, x' and three dimensional section x, y, x'. The four dimensional mass M which generates the main gravitation field of galaxy is located at the fourth dimension at the distance x' = X' and other dimensions are zero x = 0, y = 0, z = 0. The method to calculate the speed distribution curve of four dimensional mass VM: the speed distribution curve VM is calculated by using the equation in which the gravitational force is equal to the centrifugal force of rotation. The solution of this equation yields the speed distribution component VM of the four dimensional mass M and the value of the mass M. In the publication [1] has been presented rotational speed distributions curves of the galaxy NGC 3198. The speed distribution curve of galactic halo in that publication corresponds to the speed distribution curve VM of four dimensional mass M of this study. In order to find out how well this four dimensional model functions, the speed distribution curve VM of four dimensional mass M has been calculated by using two pairs of rotational radius and speed values. The conclusions and findings: the calculated distribution curve VM was a good match for the halo curve of the publication [1]. Furthermore, four rotational speed distribution curve VM was calculated using different values of the distance X', which yielded different values for the maximum radius of galaxy. In this manner the different galaxy models of the publication [2] were obtained. By that means the solution of dark matter mystery has been proved.

Comments on Warm Dark Matter Measurements and Limits

Observed spiral galaxy rotation curves allow a measurement of the warm dark matter particle velocity dispersion and mass. The measured thermal relic mass mh ≈100 eV is in disagreement with limits, typically in the range 1 to 4 keV. We review the measurements, update the no freeze-in and no freeze-out scenario of warm dark matter, and try to identify the cause of the discrepancies between measurements and limits.

Can the Standard Model Predict a Minimum Acceleration That Gets Rid of Dark Matter?

The standard model is considered to be very bad at predicting galaxy rotation, and this is why the hypothesis of dark matter was introduced in physics in the 20th century. However, in this paper, we show that the standard model may not be as far off as previously believed. By taking into account that gravity has an “infinite” extent in space and assessing the assumed mass in the observable universe, we obtain a minimum acceleration that gives a much closer match to observed galaxy rotations than would be expected. We will discuss whether or not this is enough to overturn the long-standing perspective on the standard model and if it could indeed provide a possible and adequate explanation of galaxy rotations.

A Modified Relativistic Model of Gravitational Propagation

A novel model of gravity is proposed and developed by modifying general relativity through propagating the gravitational field in an entirely analogous way to that of electromagnetic fields. It is therefore not a purely geometric model of gravitation, but is self-consistent, having clear causality and has the benefit of being inherently compatible with unified field theories. This model reproduces the observed almost constant rotational velocities of many galaxies as well as other large scale non-Keplerian motion. This is achieved without assuming the existence of dark matter and is made possible by modelling a rapidly rotating central star which with the inclusion of a velocity induced Doppler shift (of gravity) generates a highly anisotropic and intense, sheet like gravitational field. At extremely high gravitational fields this model remains real and finite i.e. does not generate a black hole, instead it asymptotically approaches a field limit below which light may escape. This is due to the inclusion of self-interaction of gravity in vacuum leading to a non-li nearity in the propagation of gravitational energy i.e. the effects of a gravitational field upon itself. This model is implemented computationally using an iterative finite element model. On the scale of our solar system these corrections are small and are shown not to be in obvious disagreement with high precision solar system tests.

Measurement of the Dark Matter Velocity Dispersion with Dwarf Galaxy Rotation Curves

Warm dark matter has, by definition, a velocity dispersion. Let vhms(a)=vhms(1)/a be the root-mean-square velocity of non-relativistic warm dark matter particles in the early universe at expansion parameter a. vhms(1) is an adiabatic invariant. We obtain vhms(1) in the core of 11 dwarf galaxies dominated by dark matter, from their observed rotation curves, up to a rotation and relaxation correction. We obtain a mean 0.490 km/s and standard deviation 0.160 km/s, with a distribution peaked at the lower end. We apply a mild, data driven, rotation and relaxation correction that obtains the adiabatic invariant in the core of the galaxies: vhms(1)=0.406 ±0.069 km/s. These two small relative standard deviations justify the prediction that the adiabatic invariant vhms(1) in the core of the galaxies is of cosmological origin if dark matter is warm. This result is in agreement with measurements of vhms(1) based on spiral galaxy rotation curves, galaxy ultra-violet luminosity distributions, galaxy stellar mass distributions, the formation of first galaxies, reionization, and the velocity dispersion cut-off mass.

Stellar populations in star clusters

Stellar populations contain the most important information about star cluster formation and evo- lution. Until several decades ago, star clusters were believed to be ideal laboratories for studies of simple stellar populations （SSPs）. However, discoveries of multiple stellar populations in Galactic globular clus- ters have expanded our view on stellar populations in star clusters. They have simultaneously generated a number of controversies, particularly as to whether young star clusters may have the same origin as old globular clusters. In addition, extensive studies have revealed that the SSP scenario does not seem to hold for some intermediate-age and young star clusters either, thus making the origin of multiple stellar popu- lations in star clusters even more complicated. Stellar population anomalies in numerous star clusters are well-documented, implying that the notion of star clusters as true SSPs faces serious challenges. In this review, we focus on stellar populations in massive clusters with different ages. We present the history and progress of research in this active field, as well as some of the most recent improvements, including ob- servational results and scenarios that have been proposed to explain the observations. Although our current ability to determine the origin of multiple stellar populations in star clusters is unsatisfactory, we propose a number of promising projects that may contribute to a significantly improved understanding of this subject.

Interpretation of Rotation Curves of Spiral Galaxies in Modified Teleparallel Gravity

There is a significant difference between the calculation based on the theory of general relativity and observation of rotation curves of spiral galaxies. To describe this discrepancy, two distinct theories have been proposed so far： existence of dark matter and modification of underlying gravitational theory. In the absence of dark matter, it is assumed that the theory of general relativity on galactic scales needs to be modified. This letter is devoted to explaining this difference in a modified teleparMIeI gravity. We show that modified teleparallel gravity favors flatness of rotation curves of spiral galaxies much in the same way as observation shows.

Comparing dark matter models,modified Newtonian dynamics and modified gravity in accounting for galaxy rotation curves

We compare six models（including the baryonic model,two dark matter models,two modified Newtonian dynamics models and one modified gravity model） in accounting for galaxy rotation curves.For the dark matter models,we assume NFW profile and core-modified profile for the dark halo,respectively.For the modified Newtonian dynamics models,we discuss Milgrom＇s MOND theory with two different interpolation functions,the standard and the simple interpolation functions.For the modified gravity,we focus on Moffat＇s MSTG theory.We fit these models to the observed rotation curves of 9 high-surface brightness and 9 low-surface brightness galaxies.We apply the Bayesian Information Criterion and the Akaike Information Criterion to test the goodness-of-fit of each model.It is found that none of the six models can fit all the galaxy rotation curves well.Two galaxies can be best fitted by the baryonic model without involving nonluminous dark matter.MOND can fit the largest number of galaxies,and only one galaxy can be best fitted by the MSTG model.Core-modified model fits about half the LSB galaxies well,but no HSB galaxies,while the NFW model fits only a small fraction of HSB galaxies but no LSB galaxies.This may imply that the oversimplified NFW and core-modified profiles cannot model the postulated dark matter haloes well.