HAYMAN, Z., RASSEM, M., ISMAEL, M. (2011). COSMOLOGICAL MODEL WITH ULTRARELATIVISTIC IDEAL GAS USING GRAVITATIONAL AND THERMO–MECHANICAL HAMILTONIAM FORMULATION. Al-Azhar Bulletin of Science, 22(Issue 2-B), 9-20. doi: 10.21608/absb.2011.7906
Z.M. HAYMAN; M.A. RASSEM; M.N. ISMAEL. "COSMOLOGICAL MODEL WITH ULTRARELATIVISTIC IDEAL GAS USING GRAVITATIONAL AND THERMO–MECHANICAL HAMILTONIAM FORMULATION". Al-Azhar Bulletin of Science, 22, Issue 2-B, 2011, 9-20. doi: 10.21608/absb.2011.7906
HAYMAN, Z., RASSEM, M., ISMAEL, M. (2011). 'COSMOLOGICAL MODEL WITH ULTRARELATIVISTIC IDEAL GAS USING GRAVITATIONAL AND THERMO–MECHANICAL HAMILTONIAM FORMULATION', Al-Azhar Bulletin of Science, 22(Issue 2-B), pp. 9-20. doi: 10.21608/absb.2011.7906
HAYMAN, Z., RASSEM, M., ISMAEL, M. COSMOLOGICAL MODEL WITH ULTRARELATIVISTIC IDEAL GAS USING GRAVITATIONAL AND THERMO–MECHANICAL HAMILTONIAM FORMULATION. Al-Azhar Bulletin of Science, 2011; 22(Issue 2-B): 9-20. doi: 10.21608/absb.2011.7906
COSMOLOGICAL MODEL WITH ULTRARELATIVISTIC IDEAL GAS USING GRAVITATIONAL AND THERMO–MECHANICAL HAMILTONIAM FORMULATION
1Department of Astronomy, Faculty of Science, Cairo University, Cairo, Egypt
2Department of Astronomy, Faculty of Science, Al-Azhar University, Cairo, Egypt.
Abstract
A brief review of the Hamiltonian theory of self gravitating perfect fluid, which has been established by Kijowski et al (1990), has been discussed in this work. The formulation of the spherically symmetric cosmological problem has been derived. The most general 3-dimensional metric in the case of spherically symmetric space-time has been considered. In addition, the parameters which govern the dynamics have been fixed. The dynamical equations have been derived. The problem of homogeneous Universe has been considered for the Ultrarelativistic ideal gas. The dynamical equations have been derived. Three analytical solutions have been obtained.
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