Holes in the fabric of space and time may be responsible for dark matter
Your typical, run-of-the-mill black holes have long ago been eliminated from the running as candidates for dark matter, that mysterious…
Your typical, run-of-the-mill black holes have long ago been eliminated from the running as candidates for dark matter, that mysterious substance that appears to make up a large proportion of the mass in our universe, including our own galaxy.
The reason is simple: ordinary black holes come from the collapse of stars, which means that they were originally formed from what is called baryonic matter, ordinary matter. You are made of baryons and so are black holes.
We know from studying how the universe formed that the amount of matter that can come from baryons has an upper bound. That is from a process called nucleosynthesis which is what creates all the elements we see in the universe.
Most of the light elements such as Helium, Lithium, and Hydrogen we see in the universe today were formed after the Big Bang following what is called the “radiation dominated” period. Based on the density of such elements that we see in the universe today, there can be only so much baryon density total that came out of the cosmic furnace.
Unfortunately, dark matter we observe based on measurements of galaxies’ rotation rates, for example, is far above that value (about 5% upper bound on baryons vs. 30% dark matter that we see from gravity). In order for all our measurements to make sense, dark matter cannot be made of ordinary stuff, even if that is hidden inside a black hole. Indeed, there is no serious baryonic candidate for dark matter.
Primordial Black Holes (PBHs) could have formed at the time of the Big Bang before nucleosynthesis of course, inside the radiation period. The problem with these little guys is that they are, well, little. Because they are little they actually produce quite a bit of light in the form of Hawking radiation. Hawking radiation comes from the conversion of curved spacetime near the event horizon into light, basically a process of the universe flattening out the black hole.
The rule is the smaller the black hole, the more Hawking radiation it produces. Oddly enough, this puts a major constraint on how many small primordial black holes the universe can contain without flooding the universe with their radiation. Unfortunately, all standard models of early black hole formation suggest that small ones must be considerably more common than large ones, so the larger ones must be exceedingly rare. We cannot account for dark matter with these without offering some additional physics to explain their non-standard size distribution.
WIMPS just aren’t the same these days.
These days the strongest candidates for dark matter are Weakly Interacting Massive Particles (WIMPs) and a few other types of particles like sterile neutrions and axions. In terms of explaining observation the WIMP theory offers researchers a lot of freedom since these types of matter have never been observed, and they would not be constrained by nucleosynthesis or radiation considerations because they are so weakly interacting. WIMPs, however, were originally motivated out of particle physics, specifically that compelling theory, supersymmetry, that continues to elude particle accelerator experiments and makes string theory oh so much more beautiful.
Unfortunately, with so much of the simplest forms of supersymmetry ruled out by experiment at the Large Hadron Collider, WIMPs attractiveness has waned a bit. It has also shifted to other areas of particle physics. In other words, the WIMPs of today are not the WIMPs of 10 years ago, they are far less well-defined. They are no longer natural.
Besides new particles, of course, there are dozens of dark matter candidates from superfluidity to modifications of gravitational theory. Some, such as Modified Newtonian Dynamics (MOND), have struggled to explain unusual cases such as the oddly located center of mass of the Bullet Cluster.
Astrophysics, like all physics, is a field dominated by constraints. You can dream all you want. Not every theory works. The problem is that too many still do. At some point, we will find the smoking gun, the experimentum crucis, and all the others will fall away. Still, for now, there is room for more.
5D Kaluza-Klein Solitons as Dark Matter
One candidate that has gotten little attention are objects that only appear in five dimensional spacetimes. These are essentially like 5D black holes in that they are a static, spherically symmetric solution to the 5D Einstein equations. Static means they don’t change in time (which is an okay assumption for human time frames compares to celestial bodies). Spherically symmetric means they are spherical in 3D space.
They are usually called Kaluza-Klein Solitons or sometimes just solitons. Derived in the 1950s with a great deal of the physical properties explored in the 1980s, these have never been observed (or at least not recognized as such). Yet, according to Prof. James Overduin at Towson University, they offer some attractive qualities when compared to other candidates.
5D Spacetime Explains Quantum Theory
The reason why we care about 5D spacetime is because quantum theory might be the result of our moving through an invisible 5th dimension. If we are moving in a 5th dimension, then 5D spacetime structures can form and affect the 4D spacetime we perceive without being entirely visible.
A 5th dimension may explain quantum theory
We know that the universe has four dimensions, but why only four? Why not five?medium.com
Solitons are made of ripples in the 5th dimension
Unlike black holes, which have singularities compressed into a single point in space, solitons are holes in spacetime. Their matter is clustered around the hole in a kind of cloud, unable to compress any further because spacetime literally ends.
Solitons are holes. Black holes are not. Try to keep that straight.
That isn’t the strangest thing about solitons though. In a 5D theory of spacetime, called a Kaluza-Klein Theory, there is no matter per se. Rather, matter in 4D spacetime is simply created from ripples and curvature in spacetime in the fifth dimension. In the 5D spacetime, there is nothing but vacuum.
These ripples in spacetime can take on many of the characteristics of matter because electromagnetism is included in Kaluza-Klein theory as fifth dimensional gravity. That is, Kaluza-Klein theory is a merging of Einstein’s theory of gravity and electromagnetism.
Solitons, however, do not include the part that interacts with the electromagnetic field. Rather, they are made up of ripples in another field in Kaluza-Klein theory, a scalar field (a field with one number at each point in spacetime). This is important for why they might be a candidate for dark matter.
Solitons are like clouds
Black holes are really just points surrounded by empty space. Solitons are clouds of matter formed of the fifth dimensional ripples. In 4D the matter is ultrarelativistic, which means it behaves like radiation rather than ordinary, slow, dust-like matter. Thus, a soliton in 4D appears to be a hole in spacetime surrounded by dense non-luminous radiation with density rapidly falling off (with distance to the fourth power) as you get farther from the hole. Unlike black holes, they do not have event horizons, so they are naked.
If you look at solitons as a source of dark matter, you can calculate how many of them there ought to be in a given cubic lightyear. Typically, we calculate this density as a fraction of the Comic Microwave Background (CMB) which is the light that fills the entire universe and is the earliest light we can see. Based on this calculation, the density of solitions as dark matter, if each individual one had the mass of a galaxy, would be about 100,000 less dense than the CMB.
How do we know if solitons are out there?
The first step to detecting solitons might be to try to show that the universe is indeed a 5D spacetime. That requires making tests and observations that try to tease apart predictions of Einstein’s 4D theory and Kaluza-Klein’s 5D theory.
It turns out that this to pretty hard. We can’t tell if spherical bodies such as stars, planets, and moons curve spacetime as in a 5D spacetime or as in a 4D spacetime unless they are spinning. Luckily, most celestial bodies spin. Unfortunately, they don’t spin very fast compared to, say, the speed of light, so our measurements of them have to be very precise.
The Geodetic Effect
5D theory differs from 4D in the geodetic effect. This effect, first predicted in 1916 but only measured in 2007 thanks to Gravity Probe B, occurs when the axis of rotation of a spinning gyroscope in orbit around a massive body tilts as it revolves around it. Newtonian (pre-Einstein) physics predicts that a gyroscope in orbit will line up its axis of rotation on every orbit. Einstein’s predicts that it will not. This effect occurs even when the massive body is not rotating.
The 5D theory predicts a smaller geodetic effect than the 4D. Currently, to the margin of error of the measurements of the deviations of the onboard gyros, Gravity Probe B cannot rule out either theory, but the 5D theory would need to be close to 4D, meaning very flat in the 5th dimension. That is, of course, consistent with the quantum interpretation where ripples in that dimension only become truly significant at quantum scales.
The Equivalence Principle
Indeed, tests such as of the equivalence principle, which is the equivalence between gravitational pull and acceleration, place strong constraints on the deviation from flatness of the fifth dimension (on the order of 1 in 100 million).
If a 5th dimension is responsible for quantum theory, we’d expect those ripples (deviations from flatness) to be even smaller, on the order of the Planck length (0.000000000000000000000000000000000016 meters) which is theorized to be the smallest measureable length. This would make solitons with very low density. Chances of detecting deviations from Einstein’s theory this way may only be possible through quantum rather than classical means.
Wesson, Paul S. “A new dark matter candidate: Kaluza-Klein solitons.” The Astrophysical Journal 420 (1994): L49-L52.
Wesson, Paul S., and J. Ponce de Leon. “The physical properties of Kaluza — Klein solitons.” Classical and Quantum Gravity 11.5 (1994): 1341.
Overduin, James Martin, and Paul S. Wesson. “Kaluza-klein gravity.” Physics Reports 283.5–6 (1997): 303–378.
Overduin, J. M., R. D. Everett, and P. S. Wesson. “Constraints on Kaluza–Klein gravity from Gravity Probe B.” General Relativity and Gravitation 45.9 (2013): 1723–1731.
Overduin, James M. “Solar system tests of the equivalence principle and constraints on higher-dimensional gravity.” Physical Review D 62.10 (2000): 102001.