# Find tetrad component from metric

1. Dec 26, 2012

### 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 ?

Last edited: Dec 26, 2012
2. Dec 26, 2012

### George Jones

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

3. Dec 26, 2012

### Worldline

if we do that we get lorentz metric !!

4. Dec 26, 2012

### Worldline

u mean find eigen vectors ?

5. Dec 27, 2012

### Bill_K

gμν = ηabeaμebν

Write this as a matrix equation:

gμν = eaμ ηab ebν

g = eT η e

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

6. Dec 27, 2012

### Worldline

Thank u dude !