Kruskal and Penrose diagrams for a Minkosky spacetime

[JeffOCA]

Hello

I'm looking for diagrams (Kruskal and Penrose diagrams) representing Minkosky spacetime.
I found two diagrams at http://nrumiano.free.fr/Estars/int_bh.html (the two first diagrams of the page). Do they represent a Minkowski spacetime ?

Thanks,
Jeff

 

[PeterDonis]

The first diagram looks OK, but I haven't heard the term "Kruskal diagram" used to describe such a diagram of Minkowski spacetime; I've only heard "Kruskal diagram" used to describe a diagram using Kruskal coordinates for black holes (which looks somewhat similar).

The second diagram looks similar to the one on the http://en.wikipedia.org/wiki/Penrose_diagram" . The latter form makes more sense to me since, as I understand it, Penrose diagrams are supposed to represent a "spherical" sort of coordinate system, where the spacelike dimension is radius r. In this interpretation having a left half of the diagram would correspond to a negative radius, which doesn't make sense.

 

[Entropia]

Hello Jeff,

Yes, the diagrams on the website you mentioned do represent a Minkowski spacetime. The first diagram is a Kruskal diagram, which is a way of representing the entire spacetime in a single diagram. It shows the full structure of a Minkowski spacetime, including the event horizon and the singularity at the center. The second diagram is a Penrose diagram, which is a conformal representation of a Minkowski spacetime. It is often used to study the causal structure of a spacetime.

In both diagrams, the horizontal axis represents space and the vertical axis represents time. The diagonal lines represent the paths of light rays, and the curved lines represent the paths of massive particles. The event horizon, where the gravitational pull becomes too strong for anything to escape, is represented by the diagonal line that forms a 45-degree angle with the horizontal axis. The singularity, where the curvature of spacetime becomes infinite, is represented by the point where all the diagonal lines converge.

I hope this helps clarify the diagrams for you. Minkowski spacetime is a fundamental concept in special relativity, and these diagrams are useful tools for understanding its structure and properties. Thank you for your question!