Talk:Penrose diagram

Penrose-Carter or Penrose?
I think these are also known as Carter diagrams or Penrose-Carter diagrams. I seem to recall something in the Hawking-Penrose lecture book about the origins of these names. -- Anon.

Certainly the Cambridge maths tripos papers use the term "Penrose-Carter diagram": see http://www.maths.cam.ac.uk/ppa/III/2002/III2002p75.pdf -- Anon, 9 Oct 2004 (UTC)


 * Correct, they are often called Penrose-Carter diagrams. This might even be preferrable because "Penrose diagram" is also used for a diagram depicting implications among the Petrov types of the Weyl tensor.

I would also add, that since they are more commonly called by only Penrose's name (without "Carter"), it is primarily his diagram, and when both names are used, "Penrose" would logically be put first. (I have only seen "Penrose-Carter" once, and have never seen "Carter-Penrose" before discovering this article) -- Eric B, 28 Dec 2005


 * My General Relativity lecturer (who did his undergrad at Cambridge) says that only Cambridge calls them "Penrose-Carter diagrams". Everyone else calls them Penrose diagrams, apart from Carter himself who refers to them as "space-time diagrams" apparently! Dazza79 (talk) 12:03, 7 March 2008 (UTC)

Carter
I added a reference to the original paper by Carter that featured such a diagram. An earlier work by Penrose featured a conformal compactification diagram of some sort, but I don't know whether it was a Carter-Penrose diagram per se, including such features as 45 degree light cones. At any rate, they are very often called Carter-Penrose diagrams. I had never before seen them called Penrose-Carter diagrams in the literature, but that name would also make sense.

At first I thought it might be right to move this article to the new name Carter-Penrose diagram; but on reflection, they are most often called Penrose diagrams, so the current name is appropriate.


 * Andrew Moylan 15:35, 17 Mar 2005 (UTC)

Feynman diagrams
Arent these the same as Fynemann diagrams ?


 * No. A Feynman diagram is an entirely different thing to a Carter-Penrose diagram.  Note the correct spelling of Feynman.  (I have corrected the spelling within the title of this discussion section.)
 * Andrew Moylan 05:13, 19 May 2005 (UTC)

They are definitely not the same as Feynman diagrams but they are in a way very similar. Both diagrams are used to display complex mathematical objects in a simple pictogram. Thus they provide a fast way of illustration and such enable physicists to support their discussions. Schoenenbach (talk) 09:32, 29 July 2013 (UTC)


 * Uh yea but no. Feynman diagrams correspond to very specific integrals. Given a Feynman diagram, you can write down the integral explicitly, then turn the crank till an answer falls out: typically a single number, or some functional relation between scattering angle and polarization or whatever. Penrose diagrams are not equations at all, they are simplified pictoral representations of 4D spacetime manifolds that are conformally equivalent to the actual manifold of interest. You cannot compute anything from it; at best, you can locate spatial, timelike and null infinities, and draw some Cauchy surfaces. There's really almost nothing in common between the two. 67.198.37.16 (talk) 04:38, 9 January 2019 (UTC)

Current version (Dec 18 2005) self-inconsistent
Replace 45 degree lines with lines of slope +/- representing the world sheets of spherical wavefronts. This will then be consistent with points corresponding to nested two-spheres. It might also be a good idea to read the Living Reviews paper before making further changes. Or else leave it to the overburdened experts, although I'd be glad for some well-informed help.---CH 04:35, 19 December 2005 (UTC)

Merge from Conformal infinity
Someone saw fit to create an article, Conformal infinity, by simply pasting in the abstract from a useful review at the LRR website. That should be deleted, probably by "merging" with this article. Needless to say, this article cites the review, so no need to paste in the abstract!

I would agree with anyone who complains that conformal infinity is a more logical name than Penrose diagram, but because most students will recognize the latter more readily than the former, I reluctantly advocate keeping the name, at least for now.---CH 20:02, 24 December 2005 (UTC)

As Eric B notes (below), conformal infinity is a part of a Penrose diagram. The current Wikipedia article called conformal infinity does not say anything important about the concept of conformal infinity in Penrose diagrams, so I don't think there is any need for, or possibility of, a merge between that page and this one. As someone else noted (above), the Conformal infinity article is just an abstract pasted from a scientific article. I believe the article Conformal infinity should be deleted. Andrew Moylan 13:59, 4 January 2006 (UTC)

Diagrams and other info
I sat down and made some diagrams from scratch, and added some information on how Penrose coordinates derive and differ from the prior diagrams by Minkowski and Kruskal-Szekeres (i.e. the conformal "crunching"), as well as how the diagrams are used to map black holes. But the rest of those requests I do not know about. Penrose diagrams, from what I have seen, are used primarily for black holes, and some other events in space-time. (I could probably articulate something on "black hole interior" if I had time, but that is probably better covered in the article "black hole".

I had considered doing the merger as well, but I do not understand "conformal infinity" beyond simply its being the distant points on the Penrose diagram. From the article written, there seems to be a lot more to it. Perhaps it should remain a separate article, as it seems to have some meaning on its own outside of Penrose diagrams. -- Eric B 16:30 28 Dec 2005

Needs Better Explanation
As usual when I want to find out what something is, I turn to Wikipedia. Today it was Penrose diagrams. The article starts with Minkowski space which I could mostly follow, then switches to black holes.


 * "Penrose diagrams are frequently used to illustrate the space-time environment of black holes. Singularities are denoted by a spacelike boundary, unlike the timelike boundary found on conventional space-time diagrams. This is due to the interchanging of timelike and spacelike coordinates within the horizon of a black hole (since space is uni-directional within the horizon, just as time is uni-directional outside the horizon). The singularity is represented by a spacelike boundary to make it clear that once an object has passed the horizon it will inevitably hit the singularity even if it attempts to take evasive action."

This paragraph generated more questions than answers:

- What are spacelike and timelike boundaries? - Why are singularities denoted by spacelike boundaries? - Why are timelike and spacelike coordinates interchanged in a black hole? (And what does that have to do with conformal diagrams?) - Space is uni-directional in a black-hole because the only direction you can go it towards the singularity? (Outside a black hole time is uni-directional and points to the future?)

My suggestion is to make the black-hole part more accessible. I'm not sure how to do this as I don't understand the material. Myrikhan (talk) 04:55, 4 March 2013 (UTC)


 * The words "spacelike" and "timelike" have a specific meaning is pseudoriemannian geometry, and thus should be wikilinks to some article that covers those concepts. Timelike and spacelike coordinates interchange because, in the Swarzschild metric, a minus sign shows up when you cross the event horizon. However, using the words "space" and "time" to talk about the interior of a black hole is inherently confusing, because providing a coordinate system is confusing. However, if you fall into a BH, time will go forward for you, as it normally does, until it stops, about 70 seconds in. (and space stops too.) These coordinate systems are call vierbeins. Its hard to make this accessible; even if you have a PhD physics, its still hard to understand wtf. Making it accessible to non-grad-students is .. hard. Yes, we should try, but its just .. hard. 67.198.37.16 (talk) 05:17, 9 January 2019 (UTC)

Description of "Conformal Boundary" needed
"Conformal boundary" redirects to this article, but is not discussed here. Either the redirection should be removed or this article should have a description of what a conformal boundary is, I'm not sure which. I was originally reading the article on the AdS/CFT Correspondence, which links to "Conformal boundary". Harryjohnston (talk) 23:40, 8 July 2013 (UTC)


 * The conformal boundary is the place where the conformal map vanishes. It vanishes at light-like future and past infinity. For the simplest Kruskal diagram, that would be the sloped edges of the hexagon. 67.198.37.16 (talk) 04:56, 9 January 2019 (UTC)

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Is there a relationship between the Stereographic Projection and Penrose Diagrams?
The "To-do"list for Penrose diagrams indicates that Penrose diagrams are 'just another Co-ordinate chart'. The below comments may be related to this issue:

It is clear that Penrose diagrams are a way to represent an infinite spacetime using a finite diagram. In his book "Cycles of Time", Penrose indicates that one can take the full Penrose diagram, cut it in half along the Vertical line connecting the Positive Distant Future with the 'Negative' Distant Past (though the diagrams seem to assume that BOTH the distant future AND the distant past are infinitely far away, and I am not certain whether this is what the Big Bang Theory tells us), Rotate the resulting right angled triangle 360 degrees to get a 'double ended cone' (imagine two cones with circular base stuck together at their circular bases) and then extend the sloping surfaces of the 'double ended cone' to infinity (away from the centre of the 'double ended cone') to get the full Minkowski space. Another method of representing an infinite object in a finite manner is the Stereographic Projection Stereographic projection which is conformal (Are Penrose diagrams called conformal diagrams because they are also conformal in the same sense as Stereographic Projections? - I don't see a Mathematical demonstration of this in the article, though I will think about it).

Perhaps it would be a good idea to indicate the precise Mathematical relationship between Stereographic Projections and Penrose diagrams? I imagine that a 4-sphere would be needed for a 4 dimensional spacetime, but in practice - when dealing with infinite 2-dimensional spacetime diagrams which would be a plane - we could sterographically project such a plane to the 2-sphere (an ordinary sphere). So, clearly, if we have two separate Mathematical objects describing the same thing (the infinite 2-d spacetime diagram), there must be a Mathematical function mapping between them, and then the Penrose Diagrams and the Sterographic Project must have some relationship (and, in a sense, be the 'same thing').

I understand that there is a BIG problem with this viewpoint (namely, that the infinite future, infinite past, and distant spacetimes would all be mapped to the same point, namely infinity). In which case the only thing connecting sterographic projects and Penrose diagrams is that they are just ways of finitely representing an infinite plane (though Penrose Diagrams preserve the fact that the distance spacetimes and distant future and distant past are, in some sense, distinct).

ASavantDude (talk) 19:31, 17 May 2018 (UTC)


 * Penrose diagrams are not stereographic projections. They are a certain kind of conformal map that maps timelike future infinity to a single point and spacelike infinity to a single point because that is a requirement to get an asymptotically flat spacetimes; see Ashtekar for details. For cosmology, where asymptotic spacetime is not flat, you can't use these naive diagrams. The cutting-and-rotating verbiage is semi-incoherent; Minkowski space is 4D not 3D; you have to rotate in two directions. The simplest penrose diagram is for Kruskal coordinates; it's a good homework exercise. The diagrams for the Kerr and charged BH solution are ... dated; they were "correct" before the discovery of the mass instability, but that instability violates the naive diagrams as such. Well, even the standard Kruskal-coord diagram is "wrong" when you try to describe a collapsing star with it. I am not aware of a good exposition for these diagrams for these cases. 67.198.37.16 (talk) 04:52, 9 January 2019 (UTC)