Transform Metric to Flat Spacetime: Advice & Hints

[PeroK]

Homework Statement

I have the metric $ds^2 = -X^2dT^2 + dX^2$

Find the coordinate transformation that reduces the metric to that of flat spacetime:

$ds^2 = -dt^2 + dx^2$

Homework Equations

The Attempt at a Solution

I'm not sure there's a systematic way to solve this (or in general to show that a metric is just flat spacetime in a different coordinate system). And I've not been able to guess a suitable transformation.

Any advice or hints on a technique or an inspired guess?

 

[Samy_A]

Homework Statement

I have the metric $ds^2 = -X^2dT^2 + dX^2$

Find the coordinate transformation that reduces the metric to that of flat spacetime:

$ds^2 = -dt^2 + dx^2$

Homework Equations

The Attempt at a Solution

I'm not sure there's a systematic way to solve this (or in general to show that a metric is just flat spacetime in a different coordinate system). And I've not been able to guess a suitable transformation.

Any advice or hints on a technique or an inspired guess?

Separation of variables (kind of)?
$t=Xf(T)$
$x=Xh(T)$
Using the transformation rules for the metric tensor leads to the expected result, but I'm not sure it is the quickest (smartest) way to do it.

 

[PeroK]

Separation of variables (kind of)?
$t=Xf(T)$
$x=Xh(T)$
Using the transformation rules for the metric tensor leads to the expected result, but I'm not sure it is the quickest (smartest) way to do it.

Yes, of course. I didn't think to try that way round. I was working with $T = T(t,x)$ etc. Many thanks.