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Although the nonlinear Schrodinger equation description of Einstein spaces has provided insights into how quantum mechanics might modify the classical general relativistic description of space-time, an exact quantum description of space-times with matter has remained elusive. In this note we outline how the nonlinear Schrodinger equation theory of Einstein spaces might be generalized to include matter by transplanting the theory to the 25+1 dimensional Lorentzian Leech lattice. Remarkably when a hexagonal section of the Leech lattice is set aside as the stage for the nonlinear Schrodinger equation, the discrete automorphism group of the complex Leech lattice with one complex direction fixed can be lifted to continuous Lie group symmetries. In this setting the wave function becomes an 11x11 complex matrix which represents matter degrees of freedom consisting of a 2-form abelian gauge field and vector nonabelian SU(3)xE6 gauge fields together with their supersymmetric partners. The lagrangian field equations for this matrix wave function appear to be a promising starting point for resolving the unphysical features inherent in the general relativistic descriptions of gravitational collapse and the big bang.
In this paper we show that the Schrodinger-Newton equation for spherically symmetric gravitational fields can be derived in a WKB-like expansion in 1/c from the Einstein-Klein-Gordon and Einstein-Dirac system.
Here, RS-II model of brane-gravity is considerd for phantom universe using non-linear equation of stste. Phantom fluid is known to violate the weak energy condition. In this paper, it is found that this characteristic of phantom energy is affected dr
We re-consider the time dependent Schrodinger-Newton equation as a model for the self-gravitational interaction of a quantum system. We numerically locate the onset of gravitationally induced inhibitions of dispersion of Gaussian wave packets and fin
We perform an analysis where Einsteins field equation is derived by means of very simple thermodynamical arguments. Our derivation is based on a consideration of the properties of a very small, spacelike two-plane in a uniformly accelerating motion.
The aim of this paper is to study, in dimensions 2 and 3, the pure-power non-linear Schrodinger equation with an external uniform magnetic field included. In particular, we derive a general criteria on the initial data and the power of the non-linear