Heurestic approach EFE - why are there 10 DOF?

[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

 

[PeterDonis]

Some sources

What sources? Please give specific references.

 

[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.

 

[PeterDonis]

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.

 

[PeterDonis]

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