Shell theorem

Abstract: We investigate the contributions of the Friedmann-Lema\^itre-Robertson-Walker metric of the standard cosmology as an asymptotic boundary condition on the first-order approximation of the gravitational field in Moffat's theory of modified gravity (MOG). We also consider contributions due to the fact that the MOG theory does not satisfy the shell theorem or Birkhoff's theorem, resulting in what is known as the "external field effect" (EFE). We show that while both these effects add small contributions to the radial acceleration law, the result is orders of magnitude smaller than the radial acceleration in spiral galaxies.

Abstract: We present extensions of the treatment contained in our recent paper on nonlocal Newtonian cosmology [C. Chicone and B. Mashhoon, J. Math. Phys. 57, 072501 (2016)]. That is, the implications of the recent nonlocal generalization of Einstein's theory of gravitation are further investigated within the regime of Newtonian cosmology. In particular, we treat the nonlocal problem of structure formation for a spherically symmetric expanding dust model and show numerically that as the central density contrast grows, it tends to decrease slowly with radial distance as the universe expands. The nonlocal violation of Newton's shell theorem provides a physical interpretation of our numerical results.

Abstract: In the present letter, Newton's theorem for the gravitational field outside a uniform spherical shell is considered. In particular, a purely geometric proof of proposition LXXI/theorem XXXI of Newton's Principia, which is suitable for undergraduates and even skilled high-school students, is proposed. Minimal knowledge of elementary calculus and three-dimensional Euclidean geometry are required.

Abstract: Recent research on superfluid quantum vacuum as the physical origin of universal space has opened new perspectives in astronomy and cosmology. Every stellar object is in the active relation with space and its density diminishes according to the mass-energy equivalence principle. As per Newton’s Shell Theorem, vacuum density is minimum at the surface of the stellar objects and in their centre. The density of space on the surface of the Black holes and in their centre is so low that atoms become unstable. Therefore, they disintegrate back into the elementary particles and cosmic rays. By transforming old matter into these fresh energies, black holes are rejuvenating the universe and keeping its entropy constant.