What is Ostrogradski instability?

 

In formulating a Lagrangian of gravity, I have many terms to choose from.

 

In a highly schematic notation the usual form of a Lagrangian might be,

 

[math]{D_{*}}^{2} X\times D^2 X + \frac{1}{2}( X \times D^3 X)[/math].

 

D respresents derivatives of spacetime displacements, and the X are spacetime coordinates. Alpha is a scalar constant to be determined.

 

But there are an infinitude of higher order derivatives to choose from. There are products of these terms that are perfectly happy to sit within a Lagrangian with consistent dimension.

 

It would be nice to know if Ostrogradski instability precludes these terms.

Edited December 22, 201312 yr by decraig

It would be nice to know if Ostrogradski instability precludes these terms.

Higher order terms in the Lagrangian are ruled out if you want a fundamental theory, however it is still possible to treat higher order theories as effective theories. This is the standard attitude to F( R ) type theories, they are effective theories coming from string theory.

Edited December 22, 201312 yr by ajb

I don't know what F( R ) theories are.

 

As you might have suspected, I heard of this on your web site

Edited December 29, 201311 yr by decraig

Theories of gravity that have Lagrangians that are polynomial in the Ricci scalar. They are a class of theories that contain higher order derivatives. They may be important in quantum GR as they may arise a quantum corrections to GR.