An effective action in Hamiltonian form is derived for a self-gravitating sphere of isotropic homogeneous dust. Starting from the Einstein-Hilbert action for barotropic perfect fluids and making use of the symmetry and equation of state of the matter distribution we obtain a family of reduced actions for two canonical variables, namely the radius of the sphere and its ADM energy, the latter bei...

The Snyder-de Sitter model is an extension of the Snyder to a de background. It called triply special relativity (TSR) because it based on three fundamental parameters: speed light, Planck mass, and cosmological constant. In this paper, we study dimensional DKP oscillator for spin zero one in framework algebra momentum space. By using technique vector spherical harmonics energy spectrum corresp...

We show that in the Snyder space the area of the disc and of the sphere can be quantized. It is also shown that the area spectrum of the sphere can be related to the Bekenstein conjecture for the area spectrum of a black hole horizon.

A Snyder model generated by the noncommutative coordinates and Lorentz generators closes a Lie algebra. The application of Heisenberg double construction is investigated for momenta generators. This leads to phase space model. Further, extended algebra constructed using algebra, in one dimension higher. dual pair group then formulated. Two doubles are considered, with conjugate tensorial anothe...