Could The Universe Be a Black Hole? (Script) (Patreon)

What is inside a black hole? Inevitable crushing doom? Gateways to other universes? Weird, multidimensional libraries? If you’ve ever wanted to know then you might be in luck - Some physicists have argued that you’re inside one right now.

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Einstein’s ridiculously successful general theory of relativity has never failed. But we know it must:  at the centers of black holes and at the Big Bang. Both of these involve matter being packed to infinite densities - they are singularities where the mathematics of GR breaks down. Well it turns out that black holes and the Big Bang have more in common than vexing Einstein. They have mathematical similarities that have led some physicists to believe that the big bang is in fact the singularity of an absurdly gigantic black hole. Let’s figure out how crazy this proposition really is.

First up, black holes. Collapse any chunk of matter far enough and it gets stuck in its own gravity. In general relativity, that looks like a point of infinite density surrounded by an event horizon. We can think of the event horizon as the surface where the flow of space itself is like a river moving at the speed of light. Nothing can swim against that flow. From the outside, the black hole looks like an orb of blackness at a particular location in space, due to the fact that nothing that not even light can travel back out from below the event horizon.

The universe also has a singularity and an event horizon. The singularity is the Big Bang, which we think of as a point in time at the beginning of the universe when all matter was compressed to infinite density and all points in space overlapped. From the Big Bang space expanded, and it’s still expanding. That expansion gives us our event horizon. If space is expanding evenly everywhere, then there are distant regions of the universe that are being propelled away from us faster than the speed of light. That means there’s a surface at a particular distance that represents the limit of our observations - in that we can never know about any event that happens beyond that surface. This is the cosmological event horizon. Now it’s somewhat more complicated - for example, we’re still receiving light from objects that are now beyond that horizon, because it was emitted by those objects before they crossed the horizon. Also, the accelerating expansion of the universe means the cosmological event horizon is closer to us than the spot where recession equals the speed of light. But the effect is the same: no events that happen now beyond that horizon can ever be seen.

Complications aside, there are striking similarities between the black hole and the universe. The obvious difference is that the big bang singularity seems to us to be a point of infinite density in space, while the black hole singularity is a time of infinite density that included all of space. Actually, that difference isn’t as different as it sounds. Both the big bang and black hole singularities occupy all of space - the difference is that the big bang singularity exists in the past for all of space, while the black hole singularity exists in the future for all of space. OK, that last part probably needs some explanation.

We’ve talked about an idea called geodesic incompleteness in a couple of episodes - in our recent one on the center of the universe, and also when we asked what happened before the big  bang. We’re going to need that idea again, so here’s a refresher. In general relativity, objects that are not being acted on by a force follow something called a geodesic. These are the straightest paths that can be taken through a curved spacetime. In a sense geodesics form the grid that defines the fabric of spacetime. It’s possible to define a geodesic at some point in space and time - say, the arc of a ball thrown through the air - and then you can trace that geodesic forwards and backwards. That trace will define the path of the thrown ball, but you can also extrapolate beyond the ball’s trajectory. That would be the path that the ball would follow if it could pass through the planet, or the path through the ground that could have brought the ball to its current point. And you can keep tracing the geodesic into the infinite future or all the way back to the Big Bang - it’s defined for all past and future times independently of the ball that. Geodesics generally don’t just end. Except at singularities. In fact, in GR singularities are defined as the end points of geodesics. All geodesics in the universe come together and terminate at the big bang. We call the Big Bang a past, space-like singularity because it occupies all of space. In the past.

A black hole contains a future, space-like singularity. Which means that all geodesics within a black hole spacetime end at the singularity in the future. No, that doesn’t mean you’re doomed to be crushed by a black hole. I mean, you might, but you might not. The black hole singularity is the all-encompassing future for the spacetime that lives beneath the event horizon in the same way that the big bang is the encompassing past for the outside universe.

So how do we make a black hole look more like a universe? We’ll need to make the black hole interior mathematically indistinguishable from a universe for someone inside it. The first step is to send that singularity to the past. A time-reversed black hole is easy enough. It’s a white hole, and it’s a valid a solution to the Einstein equations. Naturally we’ve discussed them before. The past, space-like singularity of the white hole is surrounded by an event horizon that is the opposite to a black hole event horizon - it can only be crossed from the inside to the outside. Space flows at the speed of light across the event horizon from within. That’s starting to look like our universe - a past, space-like singularity and an event horizon that can’t be crossed from the outside. But there’s still an “outside” in which the white hole appears as a bright, localized point in space. The outside region doesn’t share the same singularity origin as the white hole. On the other hand, anyone inside the white hole wouldn’t know that - so could they be fooled into thinking they're in a regular universe?

So how do we make a black hole look more like a universe? We’ll need to make the black hole interior mathematically indistinguishable from a universe for someone inside it. The first step is to send that singularity to the past.

A time-reversed black hole is easy enough. It’s a white hole, and it’s a valid a solution to the Einstein equations. Naturally we’ve discussed them before. The past, space-like singularity of the white hole is surrounded by an event horizon that is the opposite to a black hole event horizon - it can only be crossed from the inside to the outside. Space flows at the speed of light across the event horizon from within. That’s starting to look like our universe - a past, space-like singularity and an event horizon that can’t be crossed from the outside. But there’s still an “outside” in which the white hole appears as a bright, localized point in space. An outside that doesn’t share the same singularity origin. But what if those inside the white hole couldn’t know that?

At first glance, despite the similarities the interior of the white hole looks nothing like our universe. The white hole was “discovered” by messing around with the coordinates in the OG black hole solution by Karl Schwarzschild. Same trick gave us wormholes and mirror universes, by the way, and we mapped these weird spaces in a previous episode. The interior of this type of white hole looks nothing like our universe. For one thing its made of pure spacetime - no matter included , and it;s highly inhomogeneous. The curvature changes dramatically as you approach the singularity. But our universe appears to be highly homogeneous - matter and energy are very evenly spread out, and it was even more evenly spread out in the early universe. And the space-time curvature is nearly flat, so no crazy tidal forces.

The spacetime of our universe is well described by the Friedmann-Lemaitre-Robertson-Walker metric, which we also talked about in the center of the universe episode. But there is actually a way to fit an FLRW metric inside a black or white hole so that those inside it couldn’t tell the difference. The very first “realistic” mathematical description of a black hole formation was discovered in 1939 by Robert Oppenheimer - of atomic bomb fame - along with his student Hartland Snyder They approximated the collapse of a star by modeling it as a spherical cloud of matter with a perfectly homogeneous density and zero pressure. The thing collapses under its own gravity and an event horizon forms around it, but within the collapsing cloud the matter remains homogeneous and the spacetime is flat until it becomes the singularity.

Now real stars don’t look like this. They get denser towards the center and have plenty of pressure. But the Oppenheimer-Snyder solution gave our first insights into black hole formation. It also had a weird other property. This assumption of homogeneity and zero pressure was the same that Alexander Friedmann made when he first solved the Einstein equations for the whole universe, and it’s the assumption behind the FLRW metric. In fact you can describe the spacetime of a collapsing star by patching an FLRW metric inside a Schwarzschild metric. And that’s true even after the black hole’s event horizon forms. You can have what looks like a black hole from the inside, but looks like comfortably flat space inside the still-collapsing star.

If it works for the black hole then it should work for the white hole. Just flip the time axis and you have a white hole containing a bubble of expanding space that looks much like our own. If such a white hole was big enough, it could look like our universe. This was the basic proposal by Indian physicist Raj Pathria in his Black Hole Cosmology hypothesis back in 1972. As far as I’ve been able to tell, no one has convincingly shown that this can’t be true. There’s also the idea that universes are born as white holes produced after the collapse of a black hole. That’s the Cosmological Natural Selection idea by Lee Smolin, and yeah, we did an episode. In that case, black holes don’t form singularities, but rather bound back out again to create a new spacetimes from the resulting white hole - which itself creates new black holes, etc.

OK, so we need one last ingredient to be able to answer “maybe” to the question we started with: Are we in a black hole? In 1999, Stephen Hawking once showed that if a black hole is leaking its mass via Hawking radiation in perfect equilibrium with the radiation that it absorbs - for example, from the cosmic microwave background - then the line between the white hole and black hole becomes unclear. They could be the same object. If you lump all of this together - a very specific construction for white holes to make them look like our universe, and Hawking’s argument that equates them with black holes, then there’s a roundabout way to argue we might not NOT be in a black hole.

So is the universe a black hole? Or a white hole? Probably not. But not absolutely not. There’s no good reason to believe that this is the case, so we shouldn’t believe it. We’d need some deeper explanatory value to this hypothesis to really take it seriously. Cosmological natural selection might be a path to that, but we also need some evidence for that to proceed. However if we are in a black hole then there’s a huge upside: we now know what the interior of a black holes look like. And there are indeed libraries in here. Perhaps, one day, one of the books in those libraries will also answer the next question. If we’re within the event horizon of a black-slash-white hole, what’s outside? Perhaps a universe inhabited by people asking exactly the same question, with the same answer, and so on ad infinitum in a series of black holes, forming an infinitely nested space time.