# Transformation to get a metric to diagonal form

1. Jun 27, 2011

### tut_einstein

Hi,

If you have a spherically symmetric spacetime metric in a set of spherical coordinates t,r,theta,phi: [P,Q,0,0;Q,R,0,0;0,0,S,0;0,0,0,Ssin^(theta)]. Here P,Q,R,S are functions of t and r.

Now, if I want to choose cooridnates to get the metric in the generic diagonal form (that is by choosing appropriate t' and r' (the theta and phi would remain the same), is there a simple way to determine the transformation that would bring the metric to this diagonal form?

My main problem is that I'm working in a general case, where P,Q,R,S are unspecified, so I don't know their explicit dependence on t and r. I really really need help with this.

Thank you!

2. Jun 28, 2011

### holy_toaster

That is basic Linear Algebra. Works exactly the same way as diagonalisation of matrices.