I believe that the solution to the dark matter problem is primordial black holes. At the moment the most popular idea for solving the dark matter problem is WIMPS (weakly interacting massive particles). However, after decades of searching, there is no evidence that they exist. Unlike the WIMPS, there is a lot of evidence that black holes exist. We even have a picture of one! However black holes that were created as a result of stellar collapse will not solve the problem. The reason is that in Big Bang nucleosynthesis, the light elements (helium-4, helium-3, deuterium and lithium-7) were created during the first few minutes. The abundance of these light elements in the present universe requires that the abundance of protons and neutrons today to be only a few percent of the total critical density of the universe. Primordial black holes that formed within the first few seconds and acted as dark matter would be consistent with the Big Bang model.
Also, the fact that at the core of just about every galaxy we find a supermassive black hole. How did these black holes get there? Did the galaxies form first and then these black holes just found their way to the cores? That seems rather unlikely. I believe that they were there to act as seeds for galaxy formation even before stars formed. Unlike the WIMP approach, primordial black holes might explain how the supermassive black holes formed and why they are at the cores of galaxies.
So to prove this we must find primordial black holes. Stellar collapse theories predict that black holes with a mass of less than ~ 1.4 solar masses cannot form. Thus, the discovery a black hole of less than 1.4 solar masses would make a strong case for primordial black holes. We can do this by finding stars that are in orbit around such black holes. The way to do this would be measuring the stars radial velocity as a function of time. Recently a black hole of greater than 4 solar masses was found in the globular cluster NGC 3201 by making radial velocity measurements. The total change of radial velocity seen in this case exceeded 100 km/sec. I believe that such measurements are within the range possible for amateur astronomers. The real trick will be figuring out which stars to monitor. Perhaps the GAIA data base can be used to find a list of candidate stars.
I will admit this is a real long shot. However the payoff would be very large.
Edited by CygnusBob, 20 April 2019 - 06:01 PM.