Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,851 answers , 20,616 comments
1,470 users with positive rep
501 active unimported users
More ...

Is there a natural relativistic invariant representing gravitational-field strength?

+ 3 like - 0 dislike
214 views

To naturally measure the strength of the gravitational field, we cannot use $R$ or any Ricci $R_{\mu \nu}$ contraction as that yields zero even in very strong vacuum fields.

The second best candidate would be Kretschmann $K \equiv R^{\mu \nu \kappa \sigma} R_{\mu \nu \kappa \sigma}$ which is non-zero even in vacuum. However, the Kretschmann scalar is not positive definite. Apart from some rather pathological cases the change of sign of the Kretschmann scalar is associated with the switching of "gravitoelectric" and "gravitomagnetic" dominance e.g. in the Kerr space-time. This is true also for the other two usually considered scalars, Chern-Pontryagin and Euler. (Ref.)

We could obviously take $K^2$ or the absolute value $|K|$ but that doesn't change the fact that the value touches zero in extremely strong fields and thus misrepresents the field-strength. I am not really acquainted with the other scalars but it seems to me that at least all the Lovelock invariants will have very similar properties as they must add up to various manifold characteristics under integration over any field.

I have a feeling that the nature of GR with all the local inertial systems etc. does not allow for a strictly local characterization of field strength but instead either a higher-derivative or quasi-local notion is needed. Has anybody in the literature tried to construct such an invariant or at least discuss such a possibility?

asked Apr 24, 2015 in Theoretical Physics by Void (1,505 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\varnothing$ysicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...