What is Penrose diagram: Definition and 14 Discussions

In theoretical physics, a Penrose diagram (named after mathematical physicist Roger Penrose) is a two-dimensional diagram capturing the causal relations between different points in spacetime through a conformal treatment of infinity. It is an extension of a Minkowski diagram where the vertical dimension represents time, and the horizontal dimension represents a space dimension, and slanted lines at an angle of 45° correspond to light rays


{\displaystyle (c=1)}
. The biggest difference is that locally, the metric on a Penrose diagram is conformally equivalent to the actual metric in spacetime. The conformal factor is chosen such that the entire infinite spacetime is transformed into a Penrose diagram of finite size, with infinity on the boundary of the diagram. For spherically symmetric spacetimes, every point in the Penrose diagram corresponds to a 2-dimensional sphere


{\displaystyle (\theta ,\phi )}

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  1. haushofer

    A Where exactly is the wormhole in the Kruskal-Szekeres diagram?

    Dear all, recently I was brushing up my knowledge of black holes with (among others) Zee's "Einstein gravity in a Nutshell" and encountered the analytical continuation of the Schwarzschild black hole in the famous Kruskal-Szekeres coordinates (Zee: chapter VII.2). The corresponding diagram can...
  2. P

    I Penrose Diagram for Minkowski Space-Time: Step-by-Step Guide

    I'm working through Ray d'Inverno's book "Introducing Einstein's Relativity" and I've got to the section that introduces Penrose diagrams. The first example is just Minkowski space-time. The construction goes from Schwarzschild coordinates ##t## and ##r##, to define null coordinates ##v = t +...
  3. S

    A Penrose diagram of black hole with a changing event horizon

    Dear all, I have a question on Penrose diagrams. Consider a collapsing star that forms a black hole with a Schwarzschild radius normalized to 1. What happens in the Penrose diagram when additional matter falls in? I suspect the diagram then has to look like this : When the outer shell (second...
  4. P

    A Prove 2-D Lorentzian Metric is Locally Equivalent to Standard Form

    Hi, how can I prove that any 2-dim Lorentzian metric can locally be brought to the form $$g=2 g_{uv}(u,v) \mathrm{d}u \mathrm{d}v=2 g_{uv}(-\mathrm{d}t^2+dr^2)$$ in which the light-cones have slopes one? Thanks!
  5. Elnur Hajiyev

    A Light from the singularity of a charged black hole

    According to Cosmic Sensorship Conjecture, naked singularities are prohibited in General Relativity. To my knowledge, naked singularity means light from the singularity can escape to infinity. In Reissner-Nordström metric, references say naked singularity appears only if ##GM^2<P^2+Q^2##...
  6. A

    Interesting Effect of Conformal Compactification on Geodesic

    I'm trying to understand why timelike geodesics in Anti de-Sitter space are plotted as sinusoidal waves on a Penrose diagram (a nice example of the Penrose diagram for AdS is given in Figure 2.3 of this thesis: http://www.nbi.dk/~obers/MSc_PhD_files/MortenHolm_Christensen_MSc.pdf). Bearing in...
  7. R

    Penrose Diagram for Multi-Blackhole Solutions: Reference

    Can anybody recommend a reference (paper/textbook) where I can look up the Penrose diagram for multi-black hole spacetimes or multi-center solutions? Appreciate.
  8. Jimster41

    Trouble understanding 2-side BH Penrose diagram

    I've seen this a few times now, but it's not quite sinking in? How are the left and right sides of that 2-side BH Penrose diagram disconnected but share the BH? I keep thinking you could go around the black hole. Trying to think of a metaphor that correctly captures my confusion. Picturing a...
  9. bcrowell

    Necessary conditions for a Penrose diagram?

    What conditions are necessary if it's to be possible to make a Penrose diagram for a 3+1-dimensional spacetime? It seems that rotational symmetry is not necessary, since people draw Penrose diagrams for Kerr black holes. If you don't have rotational symmetry, how do you know what 2-surface is...
  10. C

    Penrose Diagram for the Kerr Black Hole

    Hey Guys, so i was reading Hawking&Ellis a bit and still encounter always problems with the Penrose-Diagrams. Looking at the Penrose-Diagram for the rotating Kerr-Black hole (just one illustrating picture at the end) i come up the following question: Why are there TWO regions III and III ? In...
  11. B

    Understanding Penrose Diagrams - Insight & Explanation

    Hey. I was hoping that someone(s) could give me some explanation and insight into the Penrose Diagram shown below. Any links to good sites would be great, as I have not found what I am looking for. I guess, one of the things I am really wondering is: why is there a circular like...
  12. N

    Drawing Penrose diagram figures

    I need to create a figure of a Penrose diagram and I wonder if there is a dedicated program to this task. I know it's only a bunch of nested squares and lines but some people like me are simply uncapable of drawing anything by hand!
  13. A

    Question on Penrose diagram for Schwazschild metric

    Hi, I am just learning about Penrose diagrams and got confused: Why is the singularity r=0 in the Schwarzschild spacetime depicted by a horizontal line in the Penrose diagram? I thought a surface like r=0 would be timeike(as in the Reisner-Nordstrom case) rather than spacelike but obviously I...
  14. C

    Penrose Diagram for Schwarzschild

    Hi. I've got a quick question on Penrose diagrams for the Schwarzschild space-time that I'd appreciate some comments on. In standard (t,r,\theta,\phi) coordinates the Schwarzschild metric is ds^2 = -\left(1-\frac{2M}{r}\right)dt^2 + \left(1-\frac{2M}{r}\right)^{-1}dr^2 + r^2 d\Omega^2. The...