Find tetrad component from metric

[Worldline]

How can find components of tetrads from metric ?
i know the relation between tetrads and metric
g$_{μ \nu}$=η$_{ab}$e$^{a}_{μ}$e$^{b}_{\nu}$
where e$^{b}_{\nu}$ are component of tetrads , in the case of Schwarzschild that metric is diagonal , it is a easy problem but what about non-diagonal metric like kerr ?

 

[George Jones]

Consider the metric as a 4x4 symmetric matrix. Diagonalize this matrix.

 

[Worldline]

if we do that we get lorentz metric !

 

[Worldline]

u mean find eigen vectors ?

 

[Bill_K]

g_μν = η_abe^a_μe^b_ν

Write this as a matrix equation:

g_μν = e^a_μ η_ab e^b_ν

g = e^T η e

The tetrad components form the matrix necessary to transform g into η.

 

[Worldline]

Thank u dude !