Research News

Using Mathematics to Uncover the Mysteries at the Center of our Universe

September 23, 2021

Mathematical equations developed by Dr. Davide Batic, Associate Professor of Mathematics at Khalifa University, predict what may be at the center of the universe is not a Black Hole, but dark matter. 



Recent advances have captured the scientific imagination, with the first image of a black hole presented in 2019 and the 2020 Nobel Prize in Physics awarded to three physicists who proved the existence of a black hole at the center of our galaxy.


Now, Dr. Davide Batic has added to this research, publishing models that show the Nobel Prize-winning conclusion could be correct, but could also be wrong.


Dr. Batic, Associate Professor of Mathematics at Khalifa University, worked with D. Asem Abuhejleh, mathematics student at KU, and Dr. Marek Nowakowski at Universidad de los Andes, Colombia. They published their results in the European Physical Journal C.


Black holes form when the center of a very massive star collapses upon itself. As stars die, the nuclear fusion at their core runs out of fuel. This means the constant outward push that balanced the inward pull of gravity from the star’s own mass is gradually reduced. When there is no longer a balance, the star begins to collapse under its own mass. If it collapses into an infinitely small point, it becomes a black hole.


Roger Penrose, Reinhard Genzel and Andrea Ghez were awarded the 2020 Nobel Prize in Physics for their work in understanding black holes, demonstrating that they are an inevitable consequence of Albert Einstein’s general theory of relativity, and then finding them. While black holes’ potential existence was proved possible through general relativity, finding them was more complicated.


In 1965, Penrose used new tools in mathematics to prove that a star collapsing and turning into a black hole is possible. Then Genzel and Ghez provided the most convincing evidence to date of a supermassive black hole at the center of the Milky Way. They found that Sagittarius A*, the black hole in question, was tugging on the stars orbiting it, making them move in very unusual ways.


Their independent discoveries of a mass four million times more massive than the sun are considered the most convincing evidence of a black hole at the center of our galaxy.


“By observing the orbital motion of stars residing in the center of our galaxy, physicists determined that there must be a huge mass sitting at the galaxy core,” Dr. Batic said. “Because this feature was accompanied by other peculiarities in the star trajectories close to the galactic core, they concluded that this mass must be a huge black hole. However, we wanted to add an important aspect to their conclusion that they did not consider: the presence of dark matter in our galaxy.”


With dark matter, more is unknown than known. Dark energy comprises roughly 68 percent of the universe, with dark matter making up about another 27 percent. Everything else — every atom, every molecule, every bit of normal matter humanity has ever observed — adds up to less than 5 percent of the universe.


Unlike normal matter, dark matter does not interact with electromagnetic forces. It does not absorb, reflect or emit light, and its existence has been only inferred by the gravitational effect it appears to have on visible matter.


“Given a mass as big as the one estimated by Penrose, Genzel and Ghez, considering the star trajectories that they observed and taking into account that most matter in the universe is made of dark matter, can we always conclude that it’s a black hole at the galactic core?” Dr. Batic said. “The answer is: It depends! It depends on how you model dark matter.


“We discovered two scenarios: According to one model, there can be a fuzzy black hole at the center, while in the other model, there is no black hole at all, but a self-gravitating ultramassive object produced by dark matter itself.”


A black hole is a region of space where matter has collapsed in on itself and the gravitational pull is so strong that nothing, not even light, can escape. It is infinitely dense and can be billions of times more massive than the sun.


The edge of a black hole, the point of no return beyond which nothing can escape, is known as the event horizon, and anything that crosses the event horizon is carried toward the singularity at the center of the black hole.


Einstein’s general theory of relativity describes physics at a grand scale; however this theory breaks down when applied to what happens inside the singularity. At this point, quantum mechanics comes into play, describing nature at the smallest scales of atoms and subatomic particles. Unifying the two remains one of science’s greatest challenges.


“In theoretical physics, string theory is our best candidate theory, which brings together quantum mechanics and general relativity,” Dr. Batic said. “If we reimagine a black hole as a fuzzball, with no singularity and no event horizon but a big tangled ball of the strings of string theory, we can resolve the issue of reconciling the classical and quantum descriptions of a black hole.”


String theory says that the entire universe is made out of strings that vibrate in various complicated ways to create space, time and all the forces and particles we know. If a black hole is actually a ball of said strings, it wouldn’t look like a smooth featureless pit of gravity narrowing down to a single point, but instead a ball packed full of strings with a fuzzy surface. A fuzzball black hole would still be dense enough to affect the stars around it in the same way a conventional black hole would, with the same effects on spacetime and light, which is why Dr. Batic’s model can predict them.


However, when the model is tuned differently to include dark matter in the center of the galaxy, the outcome is very different, predicting a dark matter  “droplet,” which is self-gravitating with no central singularity.


A fuzzy droplet has no event horizon, no exterior. If a horizon develops, it is a fuzzy black hole. A dying star may be one way of producing a black hole, but black holes may also have been formed during the Big Bang: primordial black holes made from dark matter. These would be much smaller than the black holes we know, too small to have been produced from a star, and even smaller than our sun. Primordial black holes would also form binaries, where two black holes orbit each other, which Dr. Batic’s previous work has focused upon.


For now, scientists are yet to find a primordial black hole or a fuzzy droplet. But the math works, as evidenced by Dr. Batic.


Jade Sterling
Science Writer
23 September 2021