Kruskal Diagram Hyperbola Function

[philipp2020]

hi

If I understand it correctly, the hyperbolas in the kruskal diagram define locations with the same space time.

Now my question is, how can I make a function out of the hyperbola solved for spacetime on one side and gravity/metric tensor on the other side?

Thank you very much for an answer

Philipp

 

[philipp2020]

Maybe my question was a bit unclear...

I would like to know how the function of the blue hyperbola looks like, which can be seen on the wikipedia link below.

http://en.wikipedia.org/wiki/Kruskal–Szekeres_coordinates

 

[pervect]

I'm still not sure what you are asking, even after the clarification.

The significance of the hyperbola is that they are a plot of all points with a constant "r" value on the Kruskal diagram.

The Kruskal diagram is a set of coordinates with some useful properties - one particularly useful set of properties is that all lightlike geodesics will be straight lines on the diagram.

The particulars of the conversion from Schwarzschild coordinates to Kruskal coordinates was given in the wiki.

The metric tensor in Kruskal coordinates was also given in the wiki.

 

[Bill_K]

You want the equation of the hyperbola r = const in terms of Kruskal coordinates? Isn't it just what's given in the Definition section of your Wikipedia page, setting r = constant. Parametrically in the first two equations, V = ... and U = ..., or in the fifth equation, V² - U² = ...

 

[philipp2020]

yes thanks very much for the answer. I think I understand it now.