Principal Invariants of the Weyl Tensor

[getjonwithit]

TL;DR Summary

Are there any standard names for the principal invariants of the Weyl tensor (akin to Kreschmann, Chern-Pontryagin, etc. for the Riemann tensor)?

It's possible that this may be a better fit for the Differential Geometry forum (in which case, please do let me know). However, I'm curious to know whether anyone is aware of any standard naming convention for the two principal invariants of the Weyl tensor. For the Riemann tensor, the names of the principal invariants (i.e. Kretschmann scalar, Chern-Pontryagin scalar and Euler scalar) are at least somewhat standardised, yet from the literature search that I've been able to perform thus far, I have yet to encounter any such naming convention for the Weyl tensor invariants, which are usually simply referred to as I1 and I2. Is anyone aware of any?

(For context, this is for a computational relativity package that I'm currently developing - I'd like to have some reasonably consistent, and not totally obscure, naming convention for the various quadratic curvature invariants.)

 

[robphy]

Surely you’ve checked
https://en.m.wikipedia.org/wiki/Curvature_invariant_(general_relativity)

 

[getjonwithit]

Surely you’ve checked
https://en.m.wikipedia.org/wiki/Curvature_invariant_(general_relativity)

Yes, obviously. Why do you ask?

 

[PeterDonis]

Yes, obviously. Why do you ask?

Because that answers your question: the two Weyl tensor invariants are indeed just called I1 and I2. There is no law that says every invariant needs to be named after a person.

 

[getjonwithit]

Because that answers your question: the two Weyl tensor invariants are indeed just called I1 and I2. There is no law that says every invariant needs to be named after a person.

No, it manifestly does not answer the question: the fact that a single (introductory and rather incomplete) Wikipedia article happens not to mention something does not imply that it doesn't exist.

That same article, for instance, makes reference to the Carminati-McLenaghan invariants, yet makes no mention of the deeply related real scalar invariants of Zakhary and McIntosh for Petrov and Segre-type metrics; this omission, however, does not mean that the latter do not exist, merely that Wikipedia is not omniscient.

 

[PeterDonis]

That same article, for instance, makes reference to the Carminati-McLenaghan invariants, yet makes no mention of the deeply related real scalar invariants of Zakhary and McIntosh for Petrov and Segre-type metrics

Whatever source you are getting the information from that you mention here would likely also contain the information you're looking for, if it exists. Also, the Wikipedia article gives two references.

You could also try relativity textbooks like Wald or Hawking & Ellis that are more oriented towards geometry and geometric invariants. I'm not aware of any alternate names for the Weyl tensor invariants in either of those books, but those would be good places to check.

 

[martinbn]

Why do you need names?!