Related papers: Newtonion Quantum Gravity, WIMPs and Celestial Mec…
A Newtonian approach to quantum gravity is studied. At least for weak gravitational fields it should be a valid approximation. Such an approach could be used to point out problems and prospects inherent in a more exact theory of quantum…
This work includes two new results - principally two new constants of motion for the linearised restricted 3-body problem (e.g. for the Trojan asteroids) and an important isosceles triangle generalisation of Lagrange's equilateral triangle…
Rotation curves of spiral galaxies are known with reasonable precision for a large number of galaxies with similar morphologies. The data implies that non-Keplerian fall--off is seen. This implies that (i) large amounts of dark matter must…
We apply Feynman's principle, ``The same equations have the same solutions'', to Kepler's problem and show that Newton's dynamics in a properly curved 3-D space is identical with that described by Einstein's theory in the 3-D optical…
In the hunt for WIMPish dark matter and testing our new theory, we extend the results obtained for the Kepler problem in NQG I and NQG II to the Euler two-centre problem and to other classical Hamiltonian systems with planar periodic…
On the base of an exact solution for the static spherically symmetric Einstein equations with the quintessential dark matter, we explain the asymptotic behavior of rotation curves in spiral galaxies. The parameter of the quintessence state,…
The galactic `dark matter' effect is regarded as one of the major problems in fundamental physics. Here it is explained as a self-interaction dynamical effect of space itself, and so is not caused by an unknown form of matter. Because it…
We study neutrino spin oscillations in gravitational fields. The quasi-classical approach is used to describe the neutrino spin evolution. First we examine the case of a weak gravitational field. We obtain the effective Hamiltonian for the…
We derive an effective gravitational potential, induced by the quantum wavefunction of a physical vacuum of a self-gravitating configuration, while the vacuum itself is viewed as the superfluid described by the logarithmic quantum wave…
We perform fully relativistic calculations of binary neutron stars in corotating, circular orbit. While Newtonian gravity allows for a strict equilibrium, a relativistic binary system emits gravitational radiation, causing the system to…
We obtain the wave functions associated to the quantum Newtonian universe with a cosmological constant which is described by the Schr\"{o}dinger equation and discuss some aspects of its dynamics for all forms of energy density, namely,…
The collective dynamics of objects moving through a viscous fluid is complex and counterintuitive. A key to understanding the role of nontrivial particle shape in this complexity is the interaction of a pair of sedimenting spheroids. We…
It was recently proposed that the effects usually attributed to particle dark matter on galaxy scales are due to the displacement of dark energy by baryonic matter, a paradigm known as emergent gravity. This formalism leads to predictions…
By numerically solving the mass distribution in a rotating disk based on Newton's laws of motion and gravitation, we demonstrate that the observed flat rotation curves for most spiral galaxies correspond to exponentially decreasing mass…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…
One proposal by Verlinde \cite{Verlinde:2010hp} is that gravity is not a fundamental, but an entropic force. In this way, Verlinde has provide us with a way to derive the Newton's law of gravitation from the Bekenstein-Hawking entropy-area…
We solve the Schr\"odinger-Newton problem of Newtonian gravity coupled to a nonrelativistic scalar particle for solutions with axial symmetry. The gravitational potential is driven by a mass density assumed to be proportional to the…
We consider gravity in 3+1 spacetime dimensions coupled to $N$ scalar matter fields in a semiclassical limit where $N\to\infty$. The dynamical evolution of a black hole including the back-reaction of the Hawking radiation on the metric is…
The invariance of the Lagrangian under time translations and rotations in Kepler's problem yields the conservation laws related to the energy and angular momentum. Noether's theorem reveals that these same symmetries furnish generalized…
Newtonian gravity arises as the nonrelativistic, static, weak-field limit of some Lorentzian spacetime geometry solving the generally covariant Einstein equations for a given matter field configuration. Spacetime geometry has a local…