Question

What is the degrees of freedom of metric tensor?

Answer 1

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⭕ Degree of freedom of metric tensor - Degree of freedom of a tensor is depend on the dimensions like 2D 3D etc. Hence we all know the degree of freedom is 2^n always. So the degree of freedom varies with the dimensions of a tensor.
Also a another factor which effects the freedom degree of a tensor is either its symmetric or unsymmetric.

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Answer 2

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Here is Your answer:-

The Degree of freedom of metric tensor

As g μ ν can be taken to be symmetric, it contains 10 functions of spacetime in 4 dimensions.

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