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L. Gordon, “Riemannian Space-Time, de Donder Conditions and Gravitational Field in Flat Space-Time,” International Journal of Astronomy and Astrophysics, Vol. 3, No. 1, 2013, pp. 8-19. doi:10.4236/ijaa.2013.31002

has been cited by the following article:

• TITLE: Nexus: A Quantum Theory of Space-Time, Gravity and the Quantum Vacuum

  AUTHORS: Stuart Marongwe

  KEYWORDS: Lattice Space-Time; Graviton; Dark Energy; Dark Matter; General Relativity

  JOURNAL NAME: International Journal of Astronomy and Astrophysics, Vol.3 No.3, September 3, 2013

  ABSTRACT: One of the main problems of contemporary physics is to find a quantum description of gravity. This present approach attempts to remedy the problem through the quantization of a finite but large flat Minkowski space-time by means of Fourier expansion of the displacement four vector. By applying second quantization techniques, space-time emerges as a superposition of space-time eigen states or lattices of quantized space-time vibrations also known as gravitons. Each lattice element four vector is a graviton and traces out an elementary four volume (lattice cell). The stress-momentum tensor of each graviton defines its curvature and also the curvature of the associated lattice as described by General Relativity. The eigen states of space-time are found to be separated by a quantum of energy equal to the product of the Hubble constant and the Planck constant. The highest energy state is at Planck energies. This paper also shows that gravitons can be absorbed and emitted by the space-time lattice changing the volume of its primitive cells and that particles of observable matter are associated with a graviton whose frequency is equal to the particle’s Compton frequency which the lattice can absorb producing a perturbation in the lattice. The space-time lattice is found to be unstable and decays by radiating low energy gravitons of energy equal to the product of the Hubble constant and the Planck constant. This decay causes the space-time superstructure to expand. The graviton is seen a composite spin 2 particle made from a combination of spin half components of the displacement four vector elements. The spin symmetry of its constituent elements can breakdown to give rise to other vector or scalar bosons. Dark Matter is seen as a consequence of Bose-Einstein statistics of gravitons which results in some regions of the lattice having more energy than others.