http://arxiv.org/abs/2101.07763
The flattening of galaxy rotation curves in the weak gravity regime has been the center of scientific debate for decades. The cold dark matter ($\rm CDM$) paradigm has been posited as the standard explanation, where the mass of the dark halo $m(r) = r/Gn$ roughly increases linearly with radial distance at large distances where $G$ the gravitational constant and $n$ a dimensionless parameter which depends on the amount of baryonic matter $M$ within the galaxy. Despite numerous advances in modeling galaxy formation and evolution within the dark energy-cold dark matter ($\Lambda{\rm CDM}$) model in cosmology, a scientific consensus on the origin of the observed dependence of the dimensionless parameter $n = (GMa_{0})^{-1/2}$ on the mass of baryonic matter $M$ within the galaxy (the Tully-Fisher relation), and the connection of the cosmological constant $\Lambda$ to the acceleration parameter $a_{0} \sim (\Lambda/3)^{1/2}$ remains elusive. Here, we propose relativistic equations of gravity ($\nabla_{\nu}\mathcal{K}^{\nu}{\,\,\mu} = 8\pi GM\Psi^{*}\mathcal{D}{\mu}\Psi$, where $\mathcal{K}{\mu\nu}$ is a Hermitian tensor, $\mathcal{D}{\mu}$ a covariant derivative and $\Psi$ is a complex-valued function) which we show to not only contain Einstein Field Equations but also satisfy the Tully-Fisher relation. In the weak field limit, the gravity equations reduce to a theory of $n$ bosons (Ginzburg Landau theory) where the order parameter $\Psi$ is normalized as $\int_{0}^{1/a_{0}} dr\,4\pi r^2\Psi^*\Psi = n$ and $1/a_{0} \sim (\Lambda/3)^{-1/2}$ is the cut-off radius comparable to the size of the de Sitter universe. Our investigations have significant implications for the dark matter versus MOdified Newtonian Dynamics (MOND) debate, since we provide a framework where the Tully-Fisher relation in galaxies is satisfied within the context of Einstein’s general relativity.
G. Kanyolo and T. Masese
Wed, 20 Jan 21
27/61
Comments: 9 pages, 1 figure