The apparent gravitational presence of invisible/dark matter is a key open problem of modern cosmology.
Recent posts seek an answer as Neo-Newtonian Cosmology NNC starting with a primordial gravitational potential $\phi$ as a rapidly oscillating small amplitude perturbation of a zero potential from which mass density
- $\rho\equiv\Delta\phi\ge 0$
is created through the action of the Laplacian differential operator $\Delta$ acting in a Euclidean infinite space.
We assume a decomposition $\rho =\rho_v +\rho_{iv}$ with $\rho_v$ as substantial and localised representing visible matter, and $\rho_{iv}$ as small and distributed representing invisible/dark matter with clear separation. With $u=u_v+u_{iv}$ as total matter velocity decomposed into velocity $u_v$ of visible matter and $u_{iv}$ that of invisible dark matter, NNC takes the following concise form:
- $\rho_v+\rho_{iv} = \Delta\phi$ (inverse square gravitational law in differential form)
- $\dot\rho_v =-\nabla\cdot (\rho_v u_v)$ (conservation of visible matter)
- $\dot\rho_{iv} =-\nabla\cdot (\rho_{iv} u_{iv})$ (conservation of invisible/dark matter)
- $\dot u_v=-\nabla\phi$ (Newton's 2nd Law for visible matter)
- $\dot u_{iv}=-\nabla\phi$ (Newton's 2nd Law for invisible/dark matter)
- Why does the dark matter halo not gravitationally contract? Is the density too small? Is the rate of contraction very small? Is it possible that the invisible/dark matter does not react to gravitational force, only contributes to gravitational potential?
- Is the visible galaxy formed from a primordial halo by gravitational contraction of in its center into visible matter?
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