- Prove or disprove that the Kerr metric can be expressed in a set of orthogonal coordinates over some coordinate chart.
Motivation for this question stems from my understanding that a metric can always be written in orthogonal coordinates if it exists on a flat spacetime. A metric written in an orthogonal set of coordinates has no off-diagonal terms.
As an example, the Kerr metric always seems to have at least one off-diagonal term. I understand physically why the off-diagonal terms are present in specific coordinates, but people seem to take it as a fact that it can never be transformed away or they say it is obvious that it can be.
So, since the Kerr spacetime has curvature, it makes sense that the Kerr metric cannot be written in a global set of coordinates. However, why can the metric not be written in a set of orthogonal coordinates?
Is it as simple as using a co-rotating timelike observer near infinity to be able to transform away the off-diagonal term(s) of the Kerr metric?
This question was similarly asked here, but the answers were unsatisfying because they are all stated as fact without citation or proof.
Lastly, would this be better for the Mathematics Stack Exchange? Is it purely a question of differential geometry?