# Silly doubt on penrose diagram for evaporating black hole

This question is based on the naive ideia of evaporation of a black hole stated as,

After sufficient Hawking emission the black hole loses it's mass and therefore it's area, until, as a result, the spacetime becomes simply Minkowski spacetime.

Now, the penrose diagram for this phenomena is then:

But, I would like to "see an progressive evaporation". So I imagine that the dynamical picture which "results an Minkowski spacetime" after evaporation is something like:

I don't know if this is the right way to read this particular penrose diagram, but for me makes sense, since the event horizon is losing area. So how can I "see" the evaporation "occuring" looking at an penrose diagram?

• Should I change it? – M.N.Raia Sep 17 '19 at 7:16
• It's better, just for the sake of rigour. – M.N.Raia Sep 17 '19 at 7:25
• Why would you need several Penrose diagrams for a dynamical picture? The vertical axis of a Penrose diagram is already time. – Slereah Sep 17 '19 at 8:19
• @Slereah I know that, what I'm not grasping is the concept of evaporation and the vanishing $(A=0)$ event horiozon area (or, the resultant Minkowski spacetime). The dynamics of phenomena in the first penrose diagram is precisely what I'm not understanding. For instance: why we have some sort of "ladder" in this diagram? – M.N.Raia Sep 17 '19 at 9:30
• @Slereah Even though the vertical axis is time, it does make sense to ask about multiple diagrams, since different coordinate transformations can change which features are clearly shown and which are squished. Of course all the diagrams are causally equivalent, it's just a matter of what you can see well. Hamilton has some nice examples of this, e.g. jila.colorado.edu/~ajsh/bh/stpenrosebig_gif.html for a dust collapse BH (no evap) – Joe Schindler Sep 17 '19 at 16:24

This is a diagram of space and time.

Radial distance increases from left to right Time goes from bottom to top. The future timelike infinity is i+

As pointed out in the comments this already shows the evolution of the distribution of matter from past to future infinity. There is no need to use multiple diagrams.

That Penrose diagram does not represent an evaporating black hole it represents a collapsing star forming a black hole. And the matter of the black hole hitting the singularity (the horizontal r=0 line) There is no indication of Hawking radiation here.

It appers as if the blue area is changing in size and you are apparently trying to interpret it as growing and shrinking event horizon, but it is just the remnant of the stars matter. And it is shrinking the whole time! Do note that in this diagram constant size objects would look like a "lens" shape to begin with.

Penrose diagram is not very helpful for visualizing the evolution from schwarzschild spacetime to flat spacetime, because it does not really capture the curvature of space at all. The thing it represents is the possible causal future and past of certain events and it looks pretty much the same in both spacetimes, because it is flattened out in a way to keep lightcones straight diagonal lines. Think of it as a map of earth that is straightened so that latitude and longitude lines are straight. You no longer see the intrinsic curvature of the underlying space anymore.

For intuitive introduction of Penrose diagrams I recommend "Picturing Black holes" https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/black_holes_picture/index.html

And more detailed discussion can be found at Leonard Susskind's Theoretical Minimum series: https://theoreticalminimum.com/courses/general-relativity/2012/fall

• There is no indication of Hawking radiation here. The OP is right. This is specifically the Penrose diagram of an evaporating black hole. – user4552 Sep 23 '19 at 3:30