Can a tensorial analogue of gravitational force explain away the galactic rotation curves without dark matter?

The dark matter problem is one of the most pressing problems in modern physics. As there is no well-established claim from a direct detection experiment supporting the existence of the illusive dark matter that has been postulated to explain the flat rotation curves of galaxies, and since the whole issue of an alternative theory of gravity remains controversial, it may be worth to reconsider the familiar ground of general relativity (GR) itself for a possible way out. It has recently been discovered that a skew-symmetric rank-three tensor field — the Lanczos tensor field — that generates the Weyl tensor differentially, provides a proper relativistic analogue of the Newtonian gravitational force. By taking account of its conformal invariance, the Lanczos tensor leads to a modified acceleration law which can explain, within the framework of GR itself, the flat rotation curves of galaxies without the need for any dark matter whatsoever.

Gravitational lensing study of cold dark matter-led galactic halo

In this work, the spacetime geometry of the halo region in spiral galaxies is obtained considering the observed flat galactic rotation curve feature, invoking the Tully–Fisher relation and assuming the presence of cold dark matter in the galaxy. The gravitational lensing analysis is performed treating the so-obtained spacetime as a gravitational lens. It is found that the aforementioned spacetime as the gravitational lens can consistently explain the galaxy–galaxy weak gravitational lensing observations and the lensing observations of the well-known Abell 370 and Abell 2390 galaxy clusters.

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.

The Effects of Inertial Forces on the Dynamics of Disk Galaxies

When dealing with galactic dynamics, or more specifically, with galactic rotation curves, one basic assumption is always taken: the frame of reference relative to which the rotational velocities are given is assumed to be inertial. In other words, fictitious forces are assumed to vanish relative to the observational frame of a given galaxy. It might be interesting, however, to explore the outcomes of dropping that assumption; that is, to search for signatures of non-inertial behavior in the observed data. In this work, we show that the very discrepancy in galaxy rotation curves could be attributed to non-inertial effects. We derive a model for spiral galaxies that takes into account the possible influence of fictitious forces and find that the additional terms in the new model, due to fictitious forces, closely resemble dark halo profiles. Following this result, we apply the new model to a wide sample of galaxies, spanning a large range of luminosities and radii. It turns out that the new model accurately reproduces the structures of the rotation curves and provides very good fittings to the data.

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.

The Effects of Inertial Forces on the Dynamics of Disk Galaxies

When dealing with galactic dynamics, or more specifically, with galactic rotation curves, one basic assumption is always taken: the frame of reference relative to which the rotational velocities are given is assumed to be inertial. In other words, fictitious forces are assumed to vanish relative to the observational frame of a given galaxy. It might be interesting, however, to explore the outcomes of dropping that assumption; that is, to search for signatures of non-inertial behavior in the observed data. In this work, we show that the very discrepancy in galaxy rotation curves could be attributed to non-inertial effects. We derive a model for spiral galaxies that takes into account the possible influence of fictitious forces and find that the additional terms in the new model, due to fictitious forces, closely resemble dark halo profiles. Following this result, we apply the new model to a wide sample of galaxies, spanning a large range of luminosities and radii. It turns out that the new model accurately reproduces the structures of the rotation curves and provides very good fittings to the data.

Galactic Orbital Effects on Pulsar Timing

In the currently accepted paradigm, dark matter is hypothesized as an explanation of the flat rotation curves of galaxies under the assumption of virialized orbits. The use of millisecond pulsar timing as a probe of Galactic dark matter content is explored as a means of relaxing this assumption. A method of inference of the Galactic potential using the frequency derivative $\dot{\nu }$ is produced, and an estimate for a virialized Galactic rotation curve is given through direct observation of acceleration. The data set used includes 210 pulsars with known $\dot{\nu }$ and astrometric properties, a subset of which also have measured $\ddot{\nu }$. In principle, this enables the exploration of kinematic effects, but in practice, $\ddot{\nu }$ values are found to be too imprecise at present to adequately constrain radial velocities of pulsars. Additionally, surface magnetic field strengths are inferred from $\dot{\nu }$ and the magnetic spin-down contribution to $\ddot{\nu }$ is estimated. For several pulsars the radial velocity is known, and the kinematic contribution to $\ddot{\nu }$ is estimated accordingly. The binary orbital periods of PSR J1713+0747 and other binary pulsars are also used to constrain Galactic mass density models.