Homogeneous Plane Symmetric String in Barber’s Second Self Creation Theory

Homogeneous Plane Symmetric String in Barber’s Second Self Creation Theory

S. D. Kohale a., M Laxmi b & Dr. K. D. Patil c

a *, Department of Mathematics, SDCE , Selukate , Wardha -442001, India b Department of Mathematics, BDCE, Sewagram, Wardha-442001, India c Department of Mathematics, BDCE , Sewagram , Wardha-442001, India

Abstract It's determined that plane symmetric string cosmological model doesn't exist for Takabayasi string in spherical frame of reference in Barbers second self creation

where A and B are the function of cosmic time t only. The energy momentum tensor for cloud of massive string is given by

theory. The string cosmological model exists only .Thus the

T j u u j x x j

(2)

geometric string is built in spherical frame of reference in Barbers second self creation theory.

Keywords :- Plane symmetric, string, self creation theory.

1 INTRODUCTION

In recent years researchers have plenty of interest within the consequences of line like topological defects known as cosmic strings which can be created throughout natural process in early universe. Such strings would

i i i

Where is rest energy density, is the string

tension density, u i is the four velocity for the cloud of particles, xi is the four vector which represents the strings direction which is the direction of anisotropy and

p

i

i

i

i

i

i

Where p denotes particle energy density. Moreover the direction of strings satisfy the standard relations

manufacture density fluctuations

uiu xi x 1,ui x 0

(3)

on terribly giant scales and should be to blame for the

In the co moving coordinate system, we have

formation of galaxies. Latelier and Stachel[1] studied the gravitative result of cosmic strings normally theory of relativity theory. Einsteins general theory of relativity has several controversies. so several authors planned numer ousalternatives theories by modifying the overall theory

T 1 T 2 0

j

j

1 2

1 2

and Ti 0

T3

3

3

for i j

T4

4

4

(4)

of relativity theory. Self creation cosmologies planned by Barber[2] by modifying the Brans and Dicke theory and Einstein's general theory of relativity[3]. These changed theories produce the universe out of self

The quantities and are functions of t only.

3 Field equation

The field equation in Barbers self creation theory are

G

G

1 8T i

j

j

contained gravitative and matter fields. Brans has identified that

i Ri

j

j

j

j

2

gij R

(5)

Barbers initial theory isn't solely divided with

experiment however is really inconsistent . The second theory of Barber could be a modification of Einstein's

and

8 T

3

(6)

general theory of relativity to a variable G-theory and predicts native effects that square measure at intervals the experimental limits.

During this paper, we've to construct plane interchangeable string cosmological model in Barbers Second self creation theory in spherical coordinate. so the geometric string is built in spherical frame of reference in Barbers second self creation theory.

2 PLANE SYMMETRIC METRIC

where is the coupling constant to be evaluated from

experiment and is the function of t. In the limit

0 , the theory approaches to Einsteins theory in every respect.

Thus the field equations (5) & (6) for the metric (1) with

the help of (2), (3), (4) can be written as

We consider the plane symmetric metric of the form

ds2 dt 2 A2 (r 2 d 2 dr 2 ) B2 r 2 sin 2 d 2

(1)

" ' '

" ' '

"

"

A B A B 0

(7)

Thus, geometry of the universe described by the line element with suitable transformation is obtained as,

A B AB

ds2 dT 2 T 2 (dx2 dy 2 ) dz 2

A" A' 2

2

8 1

(8)

This metric represents string cosmological model for

A

A' 2

A

A' B'

geometric strings in Barbers second self creation theory.

Case II :- 0

2

8 1

(9)

For the given case, from field equation we get

A AB

A at a1 & B a2 at a1

1

1

1

Which yields the solution logat a 1a

Hereafter the dash denotes the ordinary differentiation

with respect to time.

Where a, a1 & a2 are constant of integration.

Here we observed that the sum of the rest energy density & tension density of the cloud of string vanishes.

Thus, geometry of the universe described by the line element with suitable transformation is obtained as,

ds2 dT 2 T 2 (dx2 dy 2 ) T 2 dz 2

5 CONCLUSION

It's over that

4 SOLUTIONS

In this section, we have to construct the plane symmetric string cosmological model in Barbers Second self creation theory in spherical coordinate. The system of field equations is an under determined and to make the system consistent we consider,

1 , 0

A at a1

the undiversified plane interchangeable string cosmological model doesn't exist for Takabayasi string in spherical frame of reference in Barbers second self creation theory. The string cosmological model exist only.Thus the geometric string is built in spherical frame of reference in Barbers second self creation theory. The abstraction volume of the model for the given metric is that indicated that matter within the universe whenbeing created at the initial epoch will

1

1

Then we get

and

B a 2

at a 2

increase with time. additionally the speed of growth becomes slow as

we get

Where a, a1 & a2 are constant of integration. Also

0 . Thus the Takabayasi equation of state is

timewill increase & the speed of modification decreases as time will increase.

not compatible & we get

& 0 .

Here we consider the following cases :

Case I :-

For the given case, from field equation we get

A at a1 & B a2

Which yields the solution

c a t a m1 c a t a m2

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m 3 ,

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m 3

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