Discussion of the obtained gravity equations.

Ruslan A. Sharipov. 

1 ... 8 9 10 ... ru 

We shall discuss the equations of the gravitational field in the new theory of gravity, which is called «3D-brane universe model». I am the author of this theory. Therefore, you will receive first-hand information without any distortion.

The gravity equations in the new theory are subdivided into two groups. The equations of the first group have the form

They depend on two indices i and j. When these indices are rearranged, the equations do not change. Therefore, different equations are obtained only for the following values of the indices:

(i=1,j=1), (i=1,j=2), (i=1,j=3), (i=2,j=2), (i=2,j=3), (i=3,j=3).

This means that the total number of different equations in the first group is 6. The second group of gravity equations in the new theory contains only one equation.

As a result, the total number of the gravity equations in the new theory is 7. For comparison, the number of different gravity equations in Einstein’s theory is 10.

In the gravity equations we see many indices. They are of two sorts — upper indices and lower indices. Upper indices are called contravariant indices. Lower indices are called covariant indices. If two indices are written to the right of a symbol, then this symbol denotes a matrix element. If there are two upper indices or two lower indices, then the first of them is the row number in the matrix, and the second index is the column number. If two indices are at different levels, then the upper index is the row number of the matrix, and the lower index is the column number.

The equations of gravity are differential equations, that is, they involve differentiation. In such equations, variables are divided into two types — those that are differentiated and those by which they are differentiated. We differentiate the matrices g and b, as well as the function g with two zeros. The variables by which they are differentiated are coordinates and time.

The coordinates and time here are not arbitrary. These are comoving coordinates and brane time. They are described in separate posts.

There are many other formalities in the gravity equations that are boring to discuss. If you are interested, you can look at the original article «3D-brane gravity without equidistance postulate».


 




 

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