Complex metric solutions in GR

[haushofer]

A friend of mine had the following funny question:

Imagine I have a metric ansatz with two unknown functions. The Einstein equations give both real and complex solutions for the unknown functions.

Question: Is there a decent interpretation of these complex solutions in GR?

We know about this Newman-Janis formalism in which one uses a complex metric ansatz in order to obtain rotating black holes from stationary solutions, but this is a more general situation.

Any suggestions are appreciated :)

 

[atyy]

http://www.scholarpedia.org/article/Calabi-Yau_manifold

 

[haushofer]

I know about complex geometry; I was just wondering if these solutions also can be interpreted in conventional GR :)

 

[Bill_K]

Not the Newman-Janis formalism, it's called the Newman-Penrose formalism. Well if you don't want a complex geometry then you have to get back to a real one somehow. Newman and Penrose use a complex tetrad and complex spin coefficients but wind up taking real and imaginary parts.

The NUT parameter is like an imaginary mass, and you can transform mass into NUT and vice versa by doing the gravitational analog of a duality rotation. This can be applied to more general solutions than just Kerr.

 

[George Jones]

Not the Newman-Janis formalism, it's called the Newman-Penrose formalism.

The Newman-Janis "trick" for going from Schwarzschild to Kerr uses the Newman-Penrose formalism.

 

[Bill_K]

The Newman-Janis "trick" for going from Schwarzschild to Kerr uses the Newman-Penrose formalism.

Indeed it does.

 

[yicong2011]

See:

Newman-Penrose approach to twisting degenerate metrics
By C. J. Talbothttp://www.springerlink.com/content/v551173107166777/fulltext.pdfIt is a pretty old stuff...