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

148 Pages·2017·1.8 MB·English

Sudan University of Science & Technology
College of Graduate Studies

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

A Thesis Submitted for the Fulfillment for the Requirements
of degree of doctor of Philosophy Physics
Presented by:
Mohammed Saeed Dawood Aamir Mohammed

Supervisor by:
Prof. Mubarak Dirar Abdallah

Co supervisor:
D. Ahmed Elhassan Alfaki

January 2017
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ﮏ ﮎ ﮍ ﮌ ﮋ ﮊ ﮉ ﮈﮇ ﮆ ﮅ ﮄ ﭽ
ﮛ ﮚ ﮙ ﮘﮗ ﮖ ﮕ ﮔ ﮓ ﮒ ﮑ ﮐ
ﭼ ﮜ

I
Dedication
To my mother & father …
To my wife and To my sons & daughters …
To my brothers and sisters …
To all of my family …
I dedicate this work

II
Acknowledgement
My thanks and foremost to my GOD as without his will no thing is possible. Thanks
my supervisor Prof. Mubarak Dirar Abdallah for his encourage at first and for
supervised to this thesis. Thanks to Department of Physics, College of Graduate
Studies, Sudan University of Science and Technology.

III
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.
IV
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.

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Contents
ةيلآا i.
Dedication ii.
Acknowledgement iii.
Abstract iv.
Abstract in Arabic v.
Chapter One
Introduction
1.1 Cosmology and Stars 1
1.2 Research Problem 4
1.3 Aim of the Work 4
1.4 Previous Studies 4
1.5 Presentation of the Thesis 6
Chapter Two
Stars Evolution within the Framework of
General Relativity
2.1 Introduction 7
2.2 The Equation of the Gravitation Field 7
2.3 The Field Equation for the Universe in A commoving Coordinate System 9
2.4 Generalization of Schwarzschild Metric 15
2.5 The Singularity of Schwarzschild Solution 17
2.6 Differential Equations for Stellar Structure 19
2.7 Newtonian Stars, Polytropes and White Dwarfs 24
2.8 Neutron Stars 30
2.9 Supermassive Stars 36
2.10 Stars of Uniform Density 39
2.11 Time Dependent Spherically Symmetric Field 45
2.12 Commoving Coordinates System 48
2.13 Gravitational Collapse 51
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Chapter Three
Equilibrium of Stars By Equations of Motion to Relate
Pressure and Gravity
3.1 Introduction 61
3.2 Coordinate System and the Mass Distribution 61
3.3 The Equations of Motion and Hydrostatic Equilibrium 63
3.4 Relativistic Electron Gas in Star 65
3.5 Stars Equilibrium 70
Chapter Four
Literature Review
4.1 Introduction 75
4.2 Gravitational Self Energy Mass and A model Based on Generalized 75
General Relativity
4.3 Gravitational Self Energy Mass 76
4.4 Short Range Gravitation Field Equation Solution 80
4.5 Gravitational Waves 83
4.6 Graviton Equation of Motion 84
4.7 Graviton Energy 85
4.8 Spatial and Time Dependent Scalar Curvature and Gravitational Constant 86
Quantization
Chapter Five
Stars Evolution, String Self Energy And Nonsingular
Black Hole on the Basis Generalized Special Relativity
5.1 Introduction 90
5.2 Equilibrium Conditions 90
5.3 Conditions of Stars Evolution 99
5.4 Evolution of Stars By Kinetic Theory and Quantum Physics 107
5.5 Generation of Elementary Particles Inside Black Holes 118
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