مطالعه رهيافت هاي پنج بعدي به كرانش چهار بعدي

چكيده انگليسي :

Studding 5D Approaches to 4D Gravity Maryam Nadi m nadi@ph iut ac ir Date of Submission 6 3 2011 Department of Physics Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Farhang Loran loran@cc iut ac ir Abstract In this thesis we study five dimensional approaches to four dimensional gravity These approaches consist of Kaluza Klein theory induced matter theory and Wesson s canonical model In these models the universe is assumed to be a five dimensional 5D empty spacetime In the Kaluza Klein model a 5D manifold can unify Einstein s theory of general relativity with Maxwell s theory of electromagnetism This approach is the general relativity in 5D In this model one assumes that the fifth dimension not only is small in size but also has a closed topology Einstein and Maxwell s equations in 4D can be directly obtained from the solutions of the Einstein field equations in 5D vacuum In short Kaluza Klein theory is in general a unified theory of gravity electromagnetism and a scalar field Another version of 5D relativity which is mathematically similar but physically different is the induced matter theory The induced matter theory is based on an unrestricted 5D manifold where the extra dimension and derivatives with respect to the extra coordinate are used to explain the origin of 4D matter in terms of geometry For this reason this model is sometimes called the space time matter theory 5D induced matter theory finds an algebraic expression for what is usually called the energy momentum tensor When the field equations are set to zero to correspond to a 5D space which is apparently empty a subset of them gives back the 10 Einstein field equations in 4D with sources That is there is an effective or induced 4D energy momentum tensor which has the properties of what we normally call matter but depends on the extra metric coefficients and derivatives with respect to the extra coordinate The other five field equations give back a set of four Maxwell like or conservation equations plus one scalar wave equation Wesson s canonical model corresponds to a solution of the Einstein field equations in five dimensions which from a four dimensional point of view is equivalent to a universe with a positive cosmological constant In this model the fifth direction is perpendicular to the four dimensional spacetime and is not compactified Furthermore the mass of particles in four dimensional spacetime is related to their distance from the origin in the fifth direction while all particles are assumed to be massless in the 5D space time After reviewing these models we generalize the Wesson s canonical model by adding vector fields Theses generalization is similar to the Kaluza Klein theory i e it unifies gravity and electromagnetism in the Wesson s model We show that the vector fluctuations around the Wesson s solutions are tachyonic i e the Wesson s vacuum is unstable Furthermore the geodesic equations in the 5D spacetime give the Lorentz force in four dimensions In this model all massive particles are electrically charged and the charge to mass ratio depends on the age of the universe and exponentially tends to one Key words Wesson s canonical model Five dimensional space time Cosmological constant Tachyon

نادي، مريم

مطالعه رهيافت هاي پنج بعدي به كرانش چهار بعدي

مدل كانونيك وسون , فضا زمان پنج بعدي , ثابت كيهان شناختي , تكيون