PBS Space Time

For a while back there we might be able to avoid the black hole.

They'd been lurking as shadows in our theories of gravity forever.

Enough mass crammed into a small enough space would lead to a gravitational field at the surface from which not even light could escape from the surrounding surface that we call the event horizon.

The event horizon generates paradoxes that worry physicists, and the singularity of infinite density within the black hole worries them even more.

And so many brave physicists have fought for centuries to prove that these monsters don't exist.

They hoped nature would step in to save us from the theoretical horror of ultimate gravitational collapse.

One of our final hopes is the Planck star-a ball of energy at the heart of the black hole like frozen shards of the Big Bang.

Let's hope they're real, for physics' sake.

First there were the dark stars of Mitchell and Laplace, constructed with only Newtonian gravity.

These things were gigantic-500 times the size of the sun in Mitchell's mind.

Happily they aren't possible-giant clouds of gas fragments and collapses before a dark star can form.

But any matter collapsed far enough will have an event horizon.

Those collapsing gas fragments would form black holes themselves if they were not saved by the onset of nuclear fusion as internal temperature and pressure spikes.

The resulting outflow of energy counters the gravitational crush, birthing a true star.

Which saves us until nuclear fuel runs out, then the collapse must continue.

But, happily, not to a black hole.

Not yet.

At extreme densities-think an entire star crammed into the volume of the Earth-new, strange quantum effects come to the rescue.

The electrons of the stellar core are crushed until all available quantum states are filled, and they cannot be forced together any further.

The resulting electron degeneracy pressure halts collapse once again, giving us a white dwarf.

Nature seemed to have stepped in to halt the absurdity of the black hole.

So far so good for our hero physicists.

We have Mitchell and Laplace getting us into trouble in the first place with dark stars.

Then Arthur Eddington figuring out stellar fusion to halt collapse, then Ralph Fowler applying the brand new field of quantum mechanics that gave us white dwarfs.

But then Subramanyan Chandrasekhar came along.

At only 19 years old, on an ocean voyage from India to Cambridge to begin working with Fowler, he proved that even his new boss's white dwarfs have a failure point.

For any white dwarf 40% more massive than the Sun, gravitational crush will always exceed the outward electron degeneracy pressure.

In fact by including Einstein's relativity to the quantum description, Chandra found that outward pressure no longer rises fast enough to resist the rising crush as a white dwarf gains mass, leading to runaway collapse.

Eddington was famously very annoyed by this result and disputed it.

He was convinced that nature must step in to prevent such absurdities as infinite collapse.

But Chandra was right about white dwarf collapse.

Maybe Eddington will still be right about the ultimate infinite collapse.

There's one last brief respite for collapsing stellar cores, when physicists realised that electron capture by protons would halt collapse as a neutron star.

But the salvation of the stellar core is limited.

The more massive the neutron star, the more compact it becomes.

For neutron stars over a certain mass, the surface gravity stops light from escaping and the dreaded event horizon forms.

And that's it.

We lost our battle to stop black holes a long time ago in fact.

They are real.

We've seen them in their extreme gravitational effects across the universe, and in gravitational waves, and now even in images.

They are real, and, frankly, I think that's awesome.

You might like them too-you clicked on this episode.

So what's all this about physicists wanting to avoid the event horizon?

Well people were uncomfortable with the idea of black holes for good reasons.

And the best reason emerged in the 70s when Stephen Hawking and others showed that black holes slowly radiate away their mass, shrink, and ultimately vanish.

The main problem with this is that all information of everything swallowed by the black hole is deleted in the process.

This violates a core tenet of quantum mechanics-information conservation.

The other problem with the formation of an event horizon is that there is no known process that can stop matter within it from collapsing into a point of infinite density in the center.

This singularity generates plenty of its own problems, not least of which is that in these conditions, the two theories we used to get this far-quantum mechanics and general relativity-are so conflicted that they can't be simultaneously true.

Black holes point to fundamental flaws in our theories of nature.

OK, so even if we couldn't prevent the event horizon, maybe we can at least stop the formation of the theory-breaking singularity.

New generations of physicists took up the ancient battle to save us from this theoretical catastrophe.

Most believed that the solution must lie in a union of quantum mechanics and general relativity.

For example, string theory proposed fuzzballs, in which matter unravels into its stringy weave, filling the region beneath the horizon.

And we covered that already.

Another possible solution is the Planck star.

A star of near-absolute collapse, supported in the last instant only by the grainy structure of spacetime itself.

This comes from what has been called the main competitor of string theory: loop quantum gravity.

In LQG, space at the tiniest scale is blocky.

In particular, it's built up of quantized 2-D area elements whose interplay looks like 3-D space on larger scales.

And here larger means anything significantly bigger than the Planck length-10^-35m.

If LQG is right then it should give us the same spacetime as described by general relativity on larger scales.

That needs to be true of any quantum gravity theory, but none have been completely worked out and so there's some guesswork in connecting the Planckian scale to the scale of GR.

One way to do that is using so-called semi-classical gravity, which guesses the "perturbations" to the equations of general relativity as we approach the Planck scale.

This is how Carlo Rovelli and co.

got their first picture of the Planck star.

It actually came from an effort to describe what might happen if the entire universe collapsed like a reverse big bang.

As densities become extreme enough, LQG predicts a semi-classical correction to the cosmological equations-the Friedmann equations-in which an anti-gravity-like effect emerges, causing the collapse to bounce outward.

This loop quantum cosmology is meant to describe an infinitely expanding and contracting universe, with loopy bounces between cycles.

But in 2014, Rovelli and Francesca Vidotto showed how this result for a collapsing universe could also be used to approximate the end result of the collapsing star inside a black hole.

At a certain point, outward quantum pressure causes it to bounce.

In a way it's analogous to the quantum degeneracy pressures that stopped our white dwarf and neutron stars from collapsing further.

In that case it was quantum particles unable to occupy the same energy levels.

But with the Planck star it's the quantum elements of spacetime itself doing the work.

If LQG is right, this could handily stop the wicked singularity from forming.

For a collapsing sun-mass star, the resulting object would be about one-one-trillionth of a meter.

That's small, but it's not pointlike!

It's not a singularity.

In fact, it's 23 orders of magnitude larger than the Planck scale, so, relatively gigantic.

This ultra-compressed ball of matter is the Planck star that we've been teasing.

The thing about Planck stars is that they shouldn't last for long-at least in the semi-classical description given back in 2014.

The same spacetime pressure that stops collapse also triggers catastrophic rebound.

A similar thing happens when the core of a massive star is halted by the formation of a neutron star.

The rest of the star explodes outward as a supernova.

In the case of the Planck star, the resulting rebound is a white hole.

Basically the opposite of a black hole-the time-reversal; space and the energy it contains rushing outward and an event horizon that reverses in direction.

All of this takes place in about the time it takes light to cross the size of the Planck star-which is a tiny fraction of a second.

So it sounds like our Planck star only exists for an instant after black hole formation before exploding outwards.

But in that case why do we still see black holes out there?

And why don't we see the flashes of extreme energy expected when a white hole forms?

Maybe you've seen the film Interstellar and remember that time close to a black hole event horizon slows down from the point of view of those waiting for Matthew McConaughey back on Earth.

Hours can translate to years.

Well, imagine how strong that gravitational time dilation would be from deep below the event horizon.

Strong.

A rebounding Planck star would appear frozen in that state for billions of years for anyone but the Planck star.

So there we have it-ultimate gravitational collapse foiled again in a 10^-12 m wide ball of energy that looks like the universe as it was essentially at the Big Bang.

But at least it's not point-like or even actually Planck-scale.

But we're not quite safe yet.

The description I just gave of the Planck star is over a decade old.

It involved some serious approximations.

The quantum gravity effects were approximated as a modification to the standard equations of general relativity.

And the collapsing star was approximated as a collapsing universe-which really means that the matter is smooth and infinitely extended, not really what collapsing stars look like.

Nonetheless, yet again we have a mechanism by which the collapse is halted before reaching the theoretical unpleasantness of the singularity.

And in 2024, Rovelli and Vidotti updated the picture to describe what the Planck star eventually evolves into.

Let's zoom back out to the event horizon again.

With the interior Planck star frozen by time dilation, the event horizon slowly shrinks as it leaks Hawking radiation.

Remember that this is a problem if it causes the black hole to vanish, and take our precious quantum information with it.

Now just as loop quantum gravity arrests the Planck star collapse, it also stops that final stage of evaporation of the event horizon.

In essence, the surface area of the horizon becomes quantized and can't decay any further.

That leaves us with a Planck relic-a Planck-length event horizon that's stuck that way forever.

And these are actually a possible prediction of quantum gravity in general, and of course we've talked about them before.

But what about the frozen Planck star within that Planck relic event horizon?

Now remember that the internal Planck star was much bigger than a Planck length-so trillions of times bigger than the Planck relic that is supposed to contain it.

But this is actually what happens.

Just as time dilation freezes the Planck star rebound, the enormous stretching of space within that near-point-like event horizon holds a Planck star a trillion times larger.

But the weirdness doesn't end here.

As the shrinking event horizon approaches the Planck scale, it is subject to strong quantum effects.

And one of those is the possibility of quantum tunneling from the black hole state into a white hole state.

That same white hole can also transition back into a black hole, and the cycle can repeat indefinitely, leaving our relic and the star it contains in a quantum superposition of black hole and white hole simultaneously.

Okay, we've come a long way since the gigantic dark stars of centuries ago.

Nature seems pretty intent on forming event horizons, but maybe we can narrowly avoid the singularity.

If we follow the path of loop quantum gravity, the final stage of collapse may be simultaneously near-point-like and not, flickering eternally between being about to explode and about to collapse.

As an added bonus, quantum information is preserved in a relatively gigantic pocket within that infinitesimal speck.

Oh, and these things might explain dark matter too, but that would require a terrifyingly large number of these balls of Big Bang energy locked like genies in motes of frozen spacetime.