# Heurestic approach EFE - why are there 10 DOF?

• A
binbagsss
TL;DR Summary
Some sources state we seek 10 dof ( and so ofc this is a symmetric two index tensor.

My question is why we seek 10 dof in the first place ?

Many thanks
Some sources state we seek 10 dof ( and so ofc this is a symmetric two index tensor.

My question is why we seek 10 dof in the first place ?

Many thanks

Mentor
Some sources

What sources? Please give specific references.

• Dale
New Simplicio
The number of equations is because in General Relativity there are four dimensions of spacetime.

Daverz
The metric is symmetric, so there are only 10 independent equations out of 16. That accounts for 6 degrees of freedom. The remaining 4 degrees of freedom are to allow for arbitrary coordinate transformations.

Mentor
The metric is symmetric, so there are only 10 independent equations out of 16. That accounts for 6 degrees of freedom. The remaining 4 degrees of freedom are to allow for arbitrary coordinate transformations.

No, this is not correct. First, 10 independent equations does not account for 6 degrees of freedom. Second, 4 degrees of freedom is not enough to allow for arbitrary coordinate transformations.

Mentor
In the absence of any references, this thread is closed.