Evolution of Stars and Universe within the Framework of Generalized Special Relativity Theory

Abstract

Generalized special relativistic energy expression, beside Fermi momentum and ordinary Newtonian gravity potential were used for stars equilibrium conditions. The radius which makes the energy minimum shows that stability requires the mass to be less than certain critical mass which reflects quantum gravity behavior. This condition was similar to that of general relativity, where the radius should be greater than certain critical value. This critical value was typical to that of general relativity for black hole. The equilibrium condition show that pressure and centrifugal force should counter balance attractive gravity force. It also shows that kinetic energy balances potential energy at equilibrium. This agrees with previous models. The mathematical model was simple compared to general relativity model. Generalized special relativity energy-momentum relation beside the positivity or negativity of energy were used to construct star evolution model. In the first approach short range repulsive beside long range attractive gravity force were assumed to contribute to the total energy. This shows the existence of finite self energy of matter in the form of string. It shows that the star radius was that of general relativity black hole radius. The minimization of energy with respect to potential, radius and mass shows in all cases the string nature of matter building blocks. The star evolution to become supernova or black hole was shown to be related to the relation of thermal to attractive gravity force in the same sense shown by general relativity. The conditions of star equilibrium is discussed on the basis of the relation between pressure and gravity forces. The pressure expression was found first by using Gibbs and quantum laws. This leads to an equilibrium radius that depends on particle and mass density. The star explosion requires the energy to be positive. In this case, thermal energy exceeds gravity potential. When the generalized special relativistic energy is negative contraction takes place when gravity energy exceeds the thermal one. Star equilibrium requires the radius to have critical value typical to that of black hole and the critical mass to be less than a certain critical temperature dependent mass. V Using generalized special relativity together with Newton's laws of gravitation and treating particles as quantum strings, a useful expression for self energy was found. The critical radius of a star when particles are created is that of a black hole. The critical radius and mass are dependent on the speed of light and gravitational constant. For mass formation, the radius and mass should be small which agrees with the fact that elementary particles have very small mass and radius. The formation should also takes place at Planck time which also conforms with that proposed by big bang model.