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Starts With A Bang

Ask Ethan: Are singularities physically real?

From the Big Bang to black holes, singularities are hard to avoid. The math definitely predicts them, but are they truly, physically real?
black hole baby universe
During cosmological inflation, the space contained in the inflationary region grows exponentially, doubling in all three dimensions with each tiny fraction-of-a-second that passes. Where inflation ends, a hot Big Bang ensues. But due to quantum effects, each region where a Big Bang occurs will be surrounded by more inflating, exponentially expanding space, ensuring that no two regions where hot Big Bangs occur ever collide, intersect, or overlap.
Credit: Kavli IMPU
Key Takeaways
  • Wherever you have too much mass-or-energy together in one location in space, you inevitably arrive at what's known as a singularity: a place where the laws of physics break down.
  • This occurs because Einstein's general relativity and the small-scale quantum universe don't play nice together, and predictions under those physical conditions no longer make sense.
  • However, are singularities physically real in some sense, or are they just an indication that something else, such as a quantum theory of gravity, is required? It's time to unpack what we know.

One of the most important advances in all of physics was the development of Einstein’s general relativity: our greatest and most predictively powerful theory of gravity. Replacing the idea of a “gravitational force” that acts on objects that never physically touch one another with the notion that all objects exist within the fabric of spacetime, and that the curvature of spacetime determines how those objects will move, is a concept that many — even professionals — still struggle to wrap their heads around. However, it comes along with consequences: certain configurations of matter-and-energy within spacetime inevitably lead to a condition that marks an effective “end” or “beginning” to spacetime itself, more commonly known as a singularity.

But are these singularities necessarily physically real, representing something profound that’s occurring within the Universe? Or might there be some way to avoid them, perhaps signaling a very different scenario than space and time themselves ceasing to exist? (At least, as we understand them.) That’s what Patreon supporter Cameron Sowards wants to know, as he writes in to ask:

“Why do we believe that the pre big bang state was not a singularity when it is a much higher concentration of energy than a black hole could possibly have… since the pre big bang universe was not a singularity, could the same mechanisms that prevented it from being a singularity apply to the interior of black holes?”

There’s a tremendous amount to unpack here, so let’s try and do this question justice!

black hole central singularity
Once you cross the threshold to form a black hole, everything inside the event horizon crunches down to a singularity that is, at most, one-dimensional. No 3D structures can survive intact. That’s the conventional wisdom, and has been treated as proven for over 50 years. But with rotation added into the mix, one of the assumptions of the “proof” seems to fall apart.
Credit: vchalup / Adobe Stock

The Big Bang and the question of a “first” singularity

If you start with just two basic observations — that the Universe is full of matter and energy, and also, is expanding today — you might think there’s no way out of an initial singularity. Indeed, this was first put together nearly a hundred years ago, all the way back in the 1920s. As soon as you recognize that your Universe, on the largest of cosmic scales, is roughly the same in all locations and in all directions (what astrophysicists call “homogeneous” for the first and “isotropic” for the second), then there’s a particular exact solution (and metric for spacetime) that applies within the context of general relativity: the FLRW (Friedmann–Lemaître–Robertson–Walker) metric.

This metric, which describes the spacetime of the Universe as well as its relationship to the matter and energy within it, mandates that the Universe cannot be static, but must either expand or contract. Given that observations of the recession speed (or redshift) of distant galaxies is directly proportional to their measured distance from us, this indicates that the Universe is expanding today.

If it’s expanding today, and full of matter and radiation, then that implies that in the past, the Universe was smaller but contained the same amount of “stuff” within it. Therefore, it was denser and hotter as well. The farther we extrapolate back in time, the smaller the Universe gets. And if we go all the way back to the moment where it reaches “0” for its size, we arrive at a singularity.

balloon expanding Universe
As a balloon inflates, any coins glued to its surface will appear to recede away from one another, with ‘more distant’ coins receding more rapidly than the less distant ones. Any light will redshift, as its wavelength ‘stretches’ to longer values as the balloon’s fabric expands. This visualization solidly explains cosmological redshift within the context of the expanding Universe. If the Universe is expanding today, that means it was smaller, hotter, and denser in the past: leading to the picture of the hot Big Bang. It also explains why all quanta lose kinetic energy as the Universe expands.
Credit: E. Siegel/Beyond the Galaxy

This picture held sway for most of the 20th century, having been bolstered by what are known as the four observational cornerstones of the Big Bang theory.

  1. The observation that the Universe is expanding, as shown most clearly by the redshift-distance relation discovered by Lemaître (in 1927), and then later by Robertson (in 1928), and then later again by Hubble (in 1929-1931).
  2. The formation and growth of cosmic structure in the Universe: from an early, roughly uniform state to a clumpier, more clustered state consisting of stars, galaxies, galaxy groups and clusters, and a filamentary cosmic web at later times.
  3. The existence and blackbody spectrum of a cosmic microwave background: a background of leftover radiation dating back to the hot Big Bang itself, from an epoch when the early Universe was too hot for neutral atoms to stably form; once the atoms do form, the radiation gets released, and we can observe it today.
  4. And finally, the abundance of the lightest elements and isotopes of all: hydrogen, deuterium, helium-3, helium-4, and a tiny amount of lithium-7, all forged in the crucible of the hot Big Bang, before any stars could form.

With these four pillars supporting the hot Big Bang, there was no doubt that this theory — in contrast to all other competing models — accurately describes our cosmic origins.

inflation solve horizon flatness monopole problem
In the top panel, our modern Universe has the same properties (including temperature) everywhere because they originated from a region possessing the same properties. In the middle panel, the space that could have had any arbitrary curvature is inflated to the point where we cannot observe any curvature today, solving the flatness problem. And in the bottom panel, pre-existing high-energy relics are inflated away, providing a solution to the high-energy relic problem. This is how inflation solves the three great puzzles that the Big Bang cannot account for on its own.
Credit: E. Siegel/Beyond the Galaxy

But just because this story describes our past doesn’t necessarily mean it’s “chapter 1” of the story of our Universe. There are a great many unexplained puzzles that come along with the hot Big Bang, including:

  • Why, if the Universe reached incredibly high temperatures, are there no high-energy relics from those epochs still around in our Universe today? (Historically known as “the monopole problem.”)
  • Why, because of how cosmic expansion works, was the Universe born with its expansion rate and its total energy density perfectly balanced, so that even billions of years later, it’s still perfectly spatially flat? (Historically known as “the flatness problem.”)
  • And why, when we look at different regions of the sky that have not had time to exchange information or signals with one another, even at the speed of light, do they appear to be in perfect thermal equilibrium? (Historically known as “the horizon problem.”)

In the standard hot Big Bang, there are no explanations for this. You have to simply assert that “these are the initial conditions of the Universe” with no explanation, or as Lady Gaga might say, the Universe was simply “born this way.”

However, there’s a wonderful scientific mechanism that can set up these conditions if we hypothesize an early phase to the Universe that preceded the hot Big Bang: cosmological inflation. This theory, first proposed in 1980, not only provides explanatory power for all three of these observations, it also made an incredible new set of predictions that differ from that of a hot Big Bang without inflation, including some really weird ones, that have since been observationally confirmed.

inflationary beginning big bang
The quantum fluctuations inherent to space, stretched across the Universe during cosmic inflation, gave rise to the density fluctuations imprinted in the cosmic microwave background, which in turn gave rise to the stars, galaxies, and other large-scale structures in the Universe today. This is the best picture we have of how the entire Universe behaves, where inflation precedes and sets up the Big Bang. Unfortunately, we can only access the information contained inside our cosmic horizon, which is all part of the same fraction of one region where inflation ended some 13.8 billion years ago.
Credit: E. Siegel; ESA/Planck and the DOE/NASA/NSF Interagency Task Force on CMB research

Whereas the original hot Big Bang demanded a singularity, however, the situation now becomes a lot murkier with cosmic inflation added to the mix. Whereas an expanding Universe filled with matter-and-radiation can be traced back to a singularity, in the case of an expanding Universe that’s dominated by some sort of vacuum energy — which is the case for cosmic inflation — the question of a beginning is much less clear.

Because an inflationary spacetime expands exponentially, it can’t be traced back to a singularity; only back to a progressively smaller and smaller — but still finite and non-zero — size.

Whereas a non-inflationary expanding Universe (the classical Big Bang scenario) will allow you to trace every quantum of matter or energy back so that they meet at a single point in the past (the singularity), some geodesics go back an infinite amount in inflationary spacetimes, while others pathologically blow up and/or result in curvature singularities, indicating that inflationary spacetimes, even though they go back eternally, are what’s called “past-timelike incomplete.” This suggests that something very likely preceded cosmic inflation, and although it’s the subject of a lot of interesting ongoing research, the jury is still out on whether those spacetimes must include a singularity or not.

In other words, inflation probably wasn’t “chapter 1” of our Universe’s story either, and it is not presently 100% established whether our Universe began from a singularity or not.

black hole from initial conditions
In a Universe that isn’t expanding, you can fill it with stationary matter in any configuration you like, but it will always collapse down to a black hole. Such a Universe is unstable in the context of Einstein’s gravity, and must be expanding to be stable, or we must accept its inevitable fate.
Credit: E. Siegel/Beyond the Galaxy

Black holes and their “inevitable” singularities

On the other hand, the situation is very different when it comes to black holes. In fact, it was Einstein himself who first noted that if you took any initial configuration of mass that started off at rest (what relativists idealize as “pressureless dust“) within an otherwise static spacetime, it must inevitably collapse. Not “collapse and form a dust cloud,” but collapse all the way down until it became point-like: until it formed what’s known as a Schwarzschild (non-rotating) black hole.

In the case of a spacetime that contains Schwarzschild black hole, what happens is that far away from the black hole itself, it behaves as any other mass would: deforming and distorting the fabric of spacetime, causing it to curve from its presence, the same way that any other equivalently-valued mass (whether a gas cloud, a planet, star, white dwarf, or neutron star) would deform it.

But unlike those other cases, where the mass is distributed over a large volume of spacetime, in the case of a Schwarzschild black hole, all of that mass collapses down to a single point: a singularity. Around that singularity exists an invisible boundary — a mathematical surface — known as an event horizon, which itself marks the dividing line between where an object, even one moving at the speed of light, can or cannot escape from the gravitational pull of this “hole” in spacetime.

black hole schwarzschild
Both inside and outside the event horizon of a Schwarzschild black hole, space flows like either a moving walkway or a waterfall, depending on how you want to visualize it. At the event horizon, even if you ran (or swam) at the speed of light, there would be no overcoming the flow of spacetime, which drags you into the singularity at the center. Outside the event horizon, though, other forces (like electromagnetism) can frequently overcome the pull of gravity, causing even infalling matter to escape.
Credit: Andrew Hamilton/JILA/University of Colorado

And calling it a “hole” really is appropriate in this instance. In general relativity, we often consider the behavior of what are known as “test particles,” which is to say, something that we can drop down with any property we dream up [mass (including massless), charge, spin, position and speed (including, for massless particles, the speed of light) and a direction for that speed], and ask how it evolves/behaves in the presence of this spacetime. If you want to know what happens within your spacetime — and whether you have a singularity or not, and whether your spacetime is timelike-complete in either the future or past — dropping a series of test particles, including massless ones, is one great way to find out.

In the Schwarzschild spacetime, you can have stable orbits well beyond the vicinity of the event horizon just as you can have planets orbit the Sun or stars move around a galaxy. However, if you get too close to the event horizon, that’s no longer the case. Any quantum of anything that crosses over the event horizon, regardless of its other properties, gets inevitably drawn into the central singularity in a finite (and brief) amount of time. There are no paths around this fate, and nothing that can save you from it.

In fact, the greatest contribution of famed Nobel Laureate Roger Penrose to physics, and in fact the contribution that earned him the Nobel Prize, was the demonstration of how realistic matter, from a collapsing star, actually creates an event horizon and results in a spacetime that terminates in a singularity in the future.

penrose black hole event horizon nobel
One of the most important contributions of Roger Penrose to black hole physics is the demonstration of how a realistic object in our Universe, such as a star (or any collection of matter), can form an event horizon and how all the matter bound to it will inevitably encounter the central singularity. Once an event horizon forms, the development of a central singularity is not only inevitable, it’s extremely rapid.
Credit: J. Jarnstead/Royal Swedish Academy of Sciences; annotations by E. Siegel

Wiggle room and the chance for a way out

A black hole — even the earliest, simplest conception of a black hole — meets all the necessary criteria for being a spacetime that does, in fact, terminate in a singularity. At that location, there’s a finite, non-zero amount of mass/energy that exists within a single point of infinitesimal size, and that means all the things you’d normally calculate, like density or temperature, would simply blow up and go to infinity. That’s what happens at a singularity, and it truly is a place where pathological behaviors are all that you encounter.

You might try and argue that the Universe, in reality, isn’t described by idealized Schwarzschild black holes. You can instead attempt to add more realistic ingredients, like angular momentum (or spin), and the fact that all of the realistic black holes we’ve observed seem to not only be spinning, but spin at speeds that are quite relativistic, or an appreciable fraction of the speed of light.

And that will get you somewhere: into a different spacetime known as a Kerr spacetime, rather than a Schwarzschild spacetime. A bunch of interesting things happen in this spacetime that don’t occur in the case of non-rotation, including that the event horizon splits in two, into an inner and outer event horizon. There’s also a new in-between region, outside the outer event horizon, known as an ergosphere: where energy and mass can be extracted from just beyond the event horizon.

kerr black hole spacetime
In the vicinity of a black hole, space flows like either a moving walkway or a waterfall, depending on how you want to visualize it. Unlike in the non-rotating case, the event horizon splits into two, while the central singularity gets stretched out into a one-dimensional ring. Nobody knows what occurs at the central singularity, but it only must exist if all possible paths inevitably lead to it. This is true in the non-rotating case, but is it true in the rotating case?
Credit: Andrew Hamilton/JILA/University of Colorado

However, there’s still a singularity at the center. While it changes, becoming no longer a point but rather a 1-dimensional object that’s smeared out into a circular ring, it’s still a singularity: a line of infinite density, where again those same pathologies arise, and the laws of physics break down. That attempt to wiggle out won’t get you anywhere.

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You can try to imagine that somewhere, inside the event horizon but before you get to the singularity, there’s some compact collection of matter that refuses to collapse further. But that, too, fails due to a fact of Einstein’s relativity: no signal, interaction, or force can move faster than the speed of light. If you wish to have a particle that’s closer to the singularity (from within the event horizon) push back on an outermore particle and keep it from falling in any further, it must propagate back away from the singularity. But all paths from inside the event horizon only lead further down and closer to the central singularity; you’d have to propagate faster than the speed of light to push backward. Unless we throw out relativity altogether, there’s no hope there.

Which leaves only two places left to turn if we want to try and wriggle out of this fate:

  1. We can appeal to a yet-undiscovered theory that unifies gravitation and quantum theory, like a quantum theory of gravity, and hope that somewhere down the line it allows us to make sensible calculations for what happens where, today, we can only place a singularity.
  2. Or we can follow the highly speculative (but at least mathematically plausible) idea that perhaps a black hole is actually a gateway to a newborn, baby Universe that exists within it.
black hole event horizon
From outside a black hole, all the infalling matter will emit light and is always visible, while nothing from behind the event horizon can get out. But if you were the one who fell into a black hole, your energy could conceivably re-emerge as part of a hot Big Bang in a newborn Universe.
Credit: Andrew Hamilton, JILA, University of Colorado

There are many good reasons to hold out hope for the second one, as there’s an interesting mathematical mapping between:

  1. the inside of a rotating, Kerr black hole as you fall in past the outer event horizon,
  2. and a spacetime that looks like it expands exponentially, as though it were powered by some sort of energy inherent to the fabric of space itself.

In other words, it’s possible that any infalling material into a realistic black hole will, in some sense (after being ripped apart due to tidal forces and converted into a soup of fundamental quanta), emerge once again into what it perceives as a new Universe, and might potentially experience a hot Big Bang and the resultant cosmic evolution all over again.

However, those are our only two realistic and best hopes for avoiding encountering a central singularity within every black hole. Either quantum gravity will save us (and good luck figuring that one out, as it’s perhaps the most difficult “holy grail” problem in all of theoretical physics), or there’s the possibility that falling into a black hole will chew you up and spit your remnants out in a newborn Universe on the other side. Either way, as long as we’re stuck in our Universe, and as long as the laws of general relativity hold, it appears that a singularity at the center of each black hole really is inevitable.

Send in your Ask Ethan questions to startswithabang at gmail dot com!


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