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Penrose diagram and a map of the multiverse

VARDAAN SOOD
Oct. 6, 2021

Introduction

I'm sure you must have heard a lot of stories about black holes. But I'm sure none would have been like the one you're gonna go through today. You might've heard that everything ends once you're in a black hole and that you're in for an inevitable doom that you can ever escape.

You might also sometimes wonder why we're always talking about how white holes, wormholes, and parallel universes come into play and or do they just exist as a sci-fi dream, or maybe scientists have made up such things because there has to be something canceling out black holes, therefore white holes! But today, I'll tell you on which basis these things are predicted by theoretical physicists.

We haven't discovered many things in the universe, and nor do we understand them completely. Black holes certainly contribute a great deal to that equation. Now I'm going to present to you a tool physicists use to understand black holes, which helps combine all of the fantasy sci-fi stuff I mentioned above with fundamental theoretical physics.

Earlier graphs used to demonstrate theories were depicted as simple 2d graphs, with space as the x-axis and time as the y axis, which had a lot of downsides to it, the main one being they were incapable of introducing the concept of curves in space-time. Hence they were almost useless for black holes.

All of this until Roger Penrose came up with a brilliant solution introducing a new way to look at graphs, the Carter- Penrose diagrams or simply Penrose diagrams. A Penrose diagram is a kind of space-time diagram arranged to clarify the complete causal structure of any given geometry and basically a gateway to what happens inside the system. They can be applied to various forms like collapsing stars, evaporating stars, static black holes, Schwarzschild black holes, etc., to name a few. It is important to note here that there are currently 4 main black holes that consist of many variabilities, making the volume large.

This is the most straightforward Penrose diagram that will help us understand how to apply it later. As you can see, just like an average graph, it's got space as its x-axis and time on y. There are two main points in a Penrose diagram: Light rays move at 45 degrees from the upward vertical; as they transcend space and time equally and because we have to always move at below or equal to light speed, our range of motion has to always lie between 45 to 135 degrees wrt the x-axis.

Another point is: Points at infinity (at infinite distance, or in the infinite past or future) are contained in the diagram as the curved lines come closer and closer to include inside of them infinite space-time as we approach the edges. Now that you're familiar with the Penrose diagram; Let's get the fun started.

Application:

This is a simple Penrose diagram involving a single black hole connected to the universe at some point at the edge of space-time, with its event horizon being the boundary between the two. As you cross the horizon to the point of no return, the lines of space-time start to run and warp even faster than light, there's no going back to the universe, from which you've come, using simple conventional methods, but weird and unconventional things happen inside a black hole that even breaks the universal speed limit.

What if I tell you that you could escape from a black hole even after falling in through the event horizon!??!. Yes, I'm not kidding, and this is no sci-fi story. Whatever you're going to read from here onwards may seem like sci-fi, but it all has been theoretically proven.

Once you go inside a black hole, you'll find an inner horizon called the Cauchy horizon before the singularity where the combination of centrifugal forces due to the rotation of the black hole and pressure exerted opposite to the gravity due to electromagnetic radiation, you will be ejected out of the entire black hole but if you try to push a little harder, with a lot of speed you can overcome that outward force and go inside the portal of singularity.

For now, let's skip all the stuff that happens inside our black holes and ignore the fact that you can't push yourself hard enough using current technology and that you would probably just squeeze before u get there, but still just say that we managed to escape all this opposing force and reach the singularity. Because, of course, if you don't imagine, then you're out of the black hole, and the story ends.

Once you get inside the singularity, things get very weird, the nature of energy changes, and negative energy arises as it's the opposite of black holes (Yepp, it's a wormhole or, more professionally, Einstein Rosen bridge). You get pushed out to the other side with maximum force because space-time runs in the opposite direction just as fast as it does in the black hole's singularity, resulting in faster than light travel, which further results in time travel.

Entry to Multiverse!

Now that you've traveled in time to the future, despite being in the same space as you were earlier, you turn behind, and the black hole is just not there, simply because now you're in the future. Well, congratulations, you've escaped the black hole. Still, instead of returning to your universe, for which you should have traveled to the past in the first place and hence it was impossible unless you go at faster than light speeds, you've now reached a completely new place, yessss- a white hole. You get ejected from the white hole, it's the opposite effect of a black hole, into an entirely new universe with the same laws of physics as the old one but the specifications a little more different than before. Maybe there is no milky way here, or perhaps our earth has two Suns!

So your route was like this, event horizon-Cauchy horizon(from which you get thrown back outside in normal situations)-singularity-wormhole-white hole-another universe into the future!

This is the map of the entire multiverse and extends in all directions infinitely, a multi universal theory for which Penrose was awarded the Nobel prize. There are a few things I would like to state here: This was a solution involving the Kerr black hole, all different structures have another resolution depending on their specifications, and you'll be able to attain them on the internet as you surf through.

All these specifications I'm talking about are the static nature, rotation, electric charge or no charge, single point singularity, ring singularity being a few. Also, these mentioned solutions are very sensitive to minute details; for example, if you'd have tried to resist the path after you get into the portal, you could've reached the parallel wormhole, a place where time runs backward. Minute details can have a massive effect on any detail, and the solution I mentioned could have taken a very different path at any given space or time.

I'm trying to reinstate the point that the application of Penrose diagrams is a very vast and exciting topic that goes beyond reality and may take years to understand perfectly. Though all this may seem like fiction, it's all real, for which Roger Penrose even got a Nobel prize, as I've mentioned before...

Closing words

For me, the Penrose diagram is the line between reality and science fiction. It has always amazed me and I am still trying to learn more about it. Hope you enjoyed this article

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