الفهرس 
AbstractOnly 14 pages are availabe for public view
 |  | from | 150 |  |  |
| | | from | 150 | | |
Abstract
This thesis deals with the study of the thermodynamic functions of the Universe
in Lyra geometry and general relativity. We studied some cosmological models and
observed that. In general relativity theory and in the presence of perfect fluid, we
obtained the entropy as a constant (a diabtic process). The second law of thermodynamics
tells us the entropy must increases with time. So, the general theory of
relativity is not enough to describe the entropy of the Universe in the presence of a
perfect fluid. Yet, gravitation theory of gravity based on Lyra geometry introduced
by Sen [5] we tried to explain the entropy in the presence of perfect fluid but we
found that an additional term introduced by Lyra has no effect on the entropy of the
Universe since its arises from geometry and its not a part of the energy-momentum
tensor. An alternative theory which is suitable for describing the entropy of the Universe
in the presence of perfect fluid is a self-creation theory[16]. Now, an important
question was raised, what is the physical meaning of the time components of the displacement
vectors ? If the displacement vector component is constant, it represents
a cosmological term [67]. What about the variable component β(t)? In the case of
β(t) = 0. There is no solution for Einstein field equations based on Lyra geometry.
That means, if the matter is absent β(t) = 0. For non vacuum cosmological models
we get β(t) ̸= 0. So, to give a physical meaning for β(t) we consider it a part of the
energy-momentum tensor as viscosity or electromagnetic field. We studied (FRW)
111
4.4 Conclusions & Discussion
cosmological model in Lyra geometry in different forms of the time component of the
displacement vector β and the deceleration parameter q. In the case of β = β◦ (constant)
we obtained a static cosmological model with M(t) = constant. This result is
consistence with the result obtained by Halford [67].
We have studied a plane-symmetric space-time in the existence of viscous fluid in
general relativity and Lyra geometry. For the solution introduced on Lyra geometry,
to obtain an accelerating universe we need q = −1 + 3
1+2L < 0 that is L > 1. In this
case, p, ρ and the coefficients of the bulk viscosity ξ begin with an infinite value at
T = 0, decreases toward constant values as T = T◦ and reaches zero value at the end
of the present stage this is in agreement with Big Bang theory.
We have studied the Bianchi type V I0 model in Lyra geometry and the relativity
theory. In this study, the Lyra term can not be defined as a viscosity term as in [21]
since we obtain a non-integrable equation for the change in the entropy (not a useful
choice). The suitable description of the additional term introduced by Lyra is playing
the role of a variable cosmological term in general relativity. The additional term
introduced by Lyra affects on the behaviors of the pressure and the density which
causes a change in the thermodynamic functions of the universe. The model does not
explain an accelerating universe as q > 0. If we tried to deal with an accelerating
universe we need L < 0.5 which makes the universe imaginary (not accepted). So,
the presented model represents a stage of evolution in which q > 0.