Ostrogradski instability

[decraig]

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, 2013 by decraig

[ajb]

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, 2013 by ajb

[decraig]

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, 2013 by decraig

[ajb]

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.