- #1

jgarrel

- 3

- 0

## Homework Statement

Consider the metric ds

^{2}=(u

^{2}-v

^{2})(du

^{2}-dv

^{2}). I have to find a coordinate system (t,x), such that ds

^{2}=dt

^{2}-dx

^{2}. The same for the metric: ds

^{2}=dv

^{2}-v

^{2}du

^{2}.

## Homework Equations

General coordinate transformation, ds

^{2}=g

_{ab}dx

^{a}dx

^{b}

## The Attempt at a Solution

I started with a general transformation x

^{a}→x'

^{a}so the new metric is g'

_{μν}=g

_{ab}(dx

^{a}/dx'

^{μ})(dx

^{b}/dx'

^{ν}). The components of g (old metric) and g'(new metric) are known and the unknowns are the derivatives of the old coordinates with respect to the new ones. That's where I'm stuck.