Abstract
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.
Highlights
A confirmation of the nature of dark matter (DM) remains elusive
This is not always valid since the surroundings of the star may not really be negligible and may exert strong influences on the interior of the star. Inside the star such external influences manifest through a non-vanishing ΦH, since they are not sourced by matter inside of that star. Their rotation curves had traditionally been examined by assuming that the galaxies exist in isolation, even though we know that they must be subsumed into larger-scale gravitational structures like clusters and filaments, so we must have ΦH 6= 0
It is simple to double-check that the flux of this acceleration across the surface of any pillbox surrounding the galaxy vanishes, so there is no mass sourcing it. This gravitational field is supported instead by the boundary conditions where the galactic apparent DM (aDM) halo subsumes into the aDM distribution for the entire cluster
Summary
A confirmation of the nature of dark matter (DM) remains elusive. Weakly-interacting massive particles have recently been running up against strong constraints set by the null results of direct [1,2,3]. R two parts: a “particular solution” of the inhomogeneous equation, for which ΦN = − (ρM /∆r )dV, produced by Newton’s law qualifies as one and a solution ΦH to the homogeneous version of Poisson’s equation ∇2 ΦH = 0 whose utility is to enforce boundary conditions (which need not be trivial in a cosmological context) Such a ΦH field, orphaned (not sourced by any matter), generates a gravitational acceleration −∇ΦH and, when forcibly interpreted through. The EWM and ordinary Standard Model matter are the obvious choices This desirability for two separate new ingredients is not apparent when examining the specific Friedman–Lemaitre–Robertson–Walker metric, whose oversimplifying assumption of exact isotropy artificially takes the Weyl half of GR and ρCP out of action (there is no way to arrange the principal null directions of the Weyl tensor [33] without breaking isotropy, or equivalently, one can invoke the previous sectional curvature argument). Regardless of whether this balancing act required by the compact example describes our actual universe, there is no reasoning that prevents the EWM from being present in it anyway
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
