One of the most important advances in all of physics was the development of Einsteins 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 thats 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.) Thats 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?
Theres a tremendous amount to unpack here, so lets try and do this question justice!
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. However, one interesting coordinate transformation shows that every point in the interior of this black hole maps 1-to-1 with a point on the outside, raising the mathematically interesting possibility that the interior of each black hole gives rise to a baby universe inside of it, and the possibility that our Universe itself may have arisen from a black hole in a pre-existing universe prior to our own.
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 theres 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 theres a particular exact solution (and metric for spacetime) that applies within the context of general relativity: the FLRW (FriedmannLematreRobertsonWalker) 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 its 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.
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 balloons 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.
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.
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.
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.
But just because this story describes our past doesnt necessarily mean its chapter 1 of the story of our Universe. There are a great many unexplained puzzles that come along with the hot Big Bang, including:
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, theres 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.
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.
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 thats 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 cant 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) has all of its geodesics inevitably meet at a single point in the past, rendering it a past-timelike complete spacetime, 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 are past-timelike incomplete. This suggests that something very likely preceded cosmic inflation, and although its 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 wasnt chapter 1 of our Universes story either, and it is not presently 100% established whether our Universe began from a singularity or not.
In a Universe that isnt 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 Einsteins gravity, and must be expanding to be stable, or we must accept its inevitable fate.
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 whats 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.
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.
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, thats 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 future-complete spacetime that ends in a singularity.
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, its extremely rapid.
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 complete spacetime that does, in fact, terminate in a singularity. At that location, theres a finite, non-zero amount of mass/energy that exists within a single point of infinitesimal size, and that means all the things youd normally calculate, like density or temperature, would simply blow up and go to infinity. Thats 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, isnt 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 weve 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 dont occur in the case of non-rotation, including that the event horizon splits in two, into an inner and outer event horizon. Theres 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.
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 its presence and existence cannot be avoided with our current understanding of physics.
However, theres still a singularity at the center. While it changes, becoming no longer a point but rather a 1-dimensional object thats smeared out into a circular ring, its 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 wont 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, theres some compact collection of matter that refuses to collapse further. But that, too, fails due to a fact of Einsteins relativity: no signal, interaction, or force can move faster than the speed of light. If you wish to have a particle thats 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; youd have to propagate faster than the speed of light to push backward. Unless we throw out relativity altogether, theres no hope there.
Which leaves only two places left to turn if we want to try and wriggle out of this fate:
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.
There are many good reasons to hold out hope for the second one, as theres an interesting mathematical mapping between:
In other words, its 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 its perhaps the most difficult holy grail problem in all of theoretical physics), or theres 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 were 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.
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Original post:
Ask Ethan: Are singularities physically real? - Big Think