Diffeomorphisms in Flat-Space: Are All Metric Preserving?

[jfy4]

Hi,

I'm sorry to have to ask this, but I can't seem to reason this one out by myself at the moment. Given the metric is the Minkowski spacetime, is the group of diffeomorphisms the poincare group, or are there diffeomorphisms for flat-space that are not metric preserving?

I would really appreciate your help. Thanks,

EDIT: Nevermind, sorry for making a new thread for this... I had some tea and thought it out.

 

[dextercioby]

So you reached the conclusion that there are diffeomorphisms which are not isometries ?

 

[jfy4]

yes. there are definitely diffeomorphisms that are not isometries, a lot of them even for the minkowski metric.

 

[Ben Niehoff]

Yeah, remember that passive diffeomorphisms are just coordinate changes, and I'm sure you can imagine all kinds of coordinates on Minkowski space that have nothing to do with isometries.

 

[Sam Gralla]

A diffeomorphism is just a (smooth, invertible) map from the manifold to itself. No need to even have a metric to talk about diffeomorphisms.