Until today, we have been believing black holes to be a sphere. Every planet and star in the universe is maintaining its spherical form due to gravity. But what if the planets have higher dimensions? Dimensions that we cannot see but whose effects are still real. Does the same law still apply? In three-dimensional space, black holes were meant to be a sphere. However, according to recent research, an infinite number of configurations are possible in higher dimensions.
This mathematical research has shown that there are other black hole shapes possible. According to this new research paper which is showing mathematical proof that black holes’ infinite number of shapes is possible in dimensions five and above. The paper also shows Albert Einstein’s equations of general relativity.
Marcus Khuri, a geometer at Stony Brook University and co-author of the new work along with Jordan Rainone, a recent Stony Brook math Ph.D. said: “That would automatically show that our universe is higher-dimensional,”. Moreover, he said: “So it’s now a matter of waiting to see if our experiments can detect any.”.
Black Holes Doughnut!
Speaking of black holes, this whole story begins with Stephen Hawking’s 1972 explanation that the surface of a black hole, at a fixed moment in time, must be a two-dimensional sphere. (While a black hole is a three-dimensional object, its surface has just two spatial dimensions.
Until the late 80s and early 90s, this topic has become a point of interest for every researcher. This was the point that let the researchers find the existing 10 or 11 dimensions. Thus, all mathematicians and physicists sit in conclaves to discover the existence of black holes.
Black holes are some of the most confusing predictions of Einstein’s equations. Roberto Emparan and Harvey Reall in 2002, found a solution. A highly symmetrical black hole solution to the Einstein equations in five dimensions. They called it the “black ring” which is a three-dimensional surface with the general contours of a doughnut.
If these “black-ring” were spinning at a very high speed they would just form a doughnut-like black hole. Rainone said: “If they spin too fast, they would break apart, and if they don’t spin fast enough, they would go back to being a ball,”. Emparan and Reall found a sweet spot: “Their ring was spinning just fast enough to stay as a doughnut.”. Learning about that result gave hope to Rainone, a topologist, who said: “Our universe would be a boring place if every planet, star, and black hole resembled a ball.”
A New Focus!
In 2006, Greg Galloway of the University of Miami and Richard Schoen of Stanford University, studied Hawking’s theorem to define all possible black hole shapes that could potentially make in dimensions. They include all the shapes that were acceptable in a dimension. Including the earlier demonstrated ring and a broad class of objects called lens spaces.
One of the mathematical constructions that have long been important in both geometry and topology is Lens spaces. “Among all possible shapes the universe could throw at us in three dimensions,” said Hari Kunduri, researcher of mathematical physics at McMaster University, “the sphere is the simplest, and lens spaces are the next-simplest case.” Khuri believes lens spaces as “folded-up spheres. You are taking a sphere and folding it up in a very complicated way.”
All the Black Holes!
In 2014, Hari Kunduri and James Lucietti of the University of Edinburgh confirmed the existence of a black hole of the L(2, 1) type in five dimensions.
“It’s not so hard to make a black lens,” Hari Kunduri stated. “The hard part is doing that and making space-time flat at infinity.” Their explanation about the “black lens,”, has described an “asymptotically flat” space-time which means that the curvature of space-time, which would be high in the vicinity of a black hole, approaches zero as one moves toward infinity.
In December 2022 Khuri and Rainone published a research paper. First, both mathematicians proved the existence of black holes in the fifth dimension with lens topology L(p, q). Furthermore, Khuri pointed out: “When you go to dimensions above five, the lens space is just one piece of the total topology.”. Compared to the already visually challenging lens space it contains the black hole is even more complicated.
According to their research black holes can rotate but it is not necessary. Their explanation also pertains to an asymptotically flat space-time. Their findings and research on black holes have two independent rotational symmetries (in five dimensions) to make the Einstein equations easier to solve. “It is a simplifying assumption, but one that is not unreasonable,” Rainone says. “And without it, we don’t have a paper.”
Marcus Khuri Research:
“It’s nice and original work,” Kunduri says. “They showed that all the possibilities presented by Galloway and Schoen can be explicitly realized,” earlier once the rotational symmetries are taken into account.
The next step, according to Khuri, is to investigate if lens black holes solutions can exist and be stable in the absence of matter fields. It’s impossible, according to a 2021 study by Lucietti and Fred Tomlinson, and some sort of matter field is required. However, Khuri noted that while their thesis was supported by computational evidence rather than a mathematical proof, “it is still an open question,” Khuri says.
In the meantime, a greater mystery lurks. “Are we living in a higher-dimensional realm?” Khuri enquired. The creation of miniature black holes at the Large Hadron Collider or another particle accelerator with even higher energies has been predicted by physicists to occur in the future. According to Khuri, if an accelerator-produced black hole could be found during its brief, fractional-second lifetime and was shown to have an asymmetric topology, it would be proof that our universe has more than three spatial dimensions and one temporal dimension.
In researching black holes in dimensions five and above, such a discovery might solve a different, perhaps more philosophic problem. “General relativity,” Khuri said, “has traditionally been a four-dimensional theory.”. “We are betting on the fact that general relativity is valid in higher dimensions. If any exotic [non-spherical] black holes are detected, that would tell us our bet was justified.”
