EFE Solutions: Kerr, Mass, Energy, Metric Tensor

[zepp0814]

hi every, what part of EFE are the solutions (such as kerr ) for. Since most of them if not all don't require a mass or energy In there metric equation. I always just assume it was a solution to the metric tensor. Though i do know that the swartzschild metric requires a value for mass in its swartzschild radius.

 

[zepp0814]

so also i have been reading that ds^2 is the an invariant in a solution metric what does that mean and what could be a geometric interpretation ds^2 in a metric.

 

[WannabeNewton]

The metric tensor is always the solution to the EFEs. I don't understand your question: what do you mean by 'what "part" of the EFEs is the kerr metric a solution for'? The Kerr metric is a vacuum solution to the EFEs for spherically symmetric and stationary (but not necessarily static) sources.

The line element $ds^{2}$ can be viewed as an infinitesimal arc-length. It is invariant in the sense that it is independent of the choice of coordinates.

 

[Dale]

hi every, what part of EFE are the solutions (such as kerr ) for. Since most of them if not all don't require a mass or energy In there metric equation. I always just assume it was a solution to the metric tensor. Though i do know that the swartzschild metric requires a value for mass in its swartzschild radius.

As WannabeNewton mentioned, the goal of solving the EFE is to obtain the metric. Once you have that it is an easy computation to obtain either the curvature or the stress-energy tensor.

The ones that you mention do require a stress-energy tensor, just they are dealing with the specific case of vacuum so the stress-energy tensor is 0.