Tuesday, May 07, 2019

Gargantua: The Science behind Interstellar's black hole

If there is one thing that everyone thinks they understand about black holes, it’s spaghettification. After all, it’s a popular plot device in countless sci-fi books and movies; there’s just something incredibly gripping about the image of some intrepid—or massively unlucky—soul being strung out until she is merely atoms thick.  In fact, the concept is so ingrained in the minds of scientists and the general public alike that reviewers tore the 2014 film Interstellar to shreds (see here and here) precisely because the protagonist wasn’t stretched into oblivion!


A gargantuan black hole


Perhaps they shouldn’t have been so quick with the pen. New research, published in Physical Review D, indicates that the film’s makers may have had good reason to keep astronaut Cooper alive as he encounters a black hole singularity (aside from wanting to avoid a truly terrible ending). The key lies in the specifics of Interstellar’s black hole, a rapidly-spinning supermassive giant known as Gargantua.

The first misconception to clear up, researcher Lior Burko says, is that there is only one kind of singularity. Although most of us think of a singularity as being the region of infinite density at the center of a black hole, that’s not strictly true; rather, a singularity is a region where the governing equations take on infinite values. Think of it as a rip in spacetime, a discontinuity in the equations that implies infinite forces for anyone who approaches it—and it’s these infinite forces that are key to spaghettification.* 
The basic premise is this: as an astronaut approaches a singularity, she is exposed to unbounded gravity and density functions that create such a force difference between her head and her feet that she is stretched out infinitely far until the very atoms making up her tissues break down. However, not all singularities are created equal, and that’s key.
To the best of our knowledge, the center of a black hole like Gargantua holds what’s known as a BKL singularity, named for the three scientists who discovered it. “I would recommend to anyone to stay away from that one,” Burko says grimly. The highly chaotic and destructive nature of this singularity would stretch an astronaut first in one direction, then in another, like an unpredictable taffy machine. Needless to say, there’s no chance of surviving this type of singularity.
In a charged or spinning black hole like Gargantua, though, there are a few other singularities. As an astronaut falls into such a black hole, her time is slowed down so that she can perceive the millions or billions of years’ worth of matter that falls into the black hole behind her. From her perspective, this all piles up into a virtual wall chasing her at close to the speed of light: the infalling (or mass inflation) singularity. 
Furthermore, of all the matter that has fallen into the black hole before her, a small portion is reflected off the chaotic center, much like sunlight is reflected off a tumultuous ocean surface. Similarly, this reflected matter flies towards her with incredible energy from the inside of the black hole. “It’s a sort of a shock wave, the same way you would have a supersonic boom from a jet airplane that exceeds the speed of sound,” Burko explains. This “shock wave” is known as the outflying singularity.
In other words, upon crossing the event horizon our astronaut finds herself sandwiched between two singularities hurtling towards her from all sides. So what happens when they catch up with her?


 A visualization of the three varieties of singularities present in a black hole like Gargantua (from Kip Thorne's The Science of Interstellar)


Burko and his coauthor, Gaurav Khanna, used a linearized version of the Einstein equations describing spacetime to investigate the effects of an approaching outflying singularity on an astronaut. Ever the Interstellar fans, they modeled their simulation after a fast-spinning supermassive black hole like Gargantua, although the actual parameters from the film would have made their calculation time prohibitively large.
Shockingly, they found that although the singularities by necessity carry with them infinite tidal forces, the integrated effect of an astronaut crossing the outflying singularity can be bounded. This means that even though she’s surrounded by impossibly large forces, she is only stretched a finite amount.
Of course, humans aren’t really made for stretching at all. But the point is that we can work with the finite by developing materials and spacesuits specifically for the purpose. Perhaps the bigger point for Interstellar fans is that—hypothetically—Cooper could have encountered a singularity and lived to tell the tale.
Even so, Burko is careful not to get anyone’s hopes up about actually visiting a black hole in the future. “As a physicist, I like to ask the question whether the laws of physics prohibit something,” he says of surviving an encounter with an outflying singularity of this type. “At this time we cannot rule out the possibility of using black holes as portals for hyperspace travel.” 
Burko says that the film presents three types of science: well-established science that is mainstream in the astronomical community, less certain science that is nevertheless based on educated guesses, and more speculative science (tesseract, we’re looking at you). “The most we can say about that is that we don’t have any indication that it is outright wrong,” he says with a laugh. “I think that in Interstellar they use a very healthy mix of the three in order to make a very good storyline.” This research gives at least the lack of spaghettification a boost of credibility.
Granted, these simulations are limited by the fact that they are based merely upon an approximation of the Einstein equations. Burko admits that this is a weakness of the study, but he also sees it as a major advantage because it allows for longer simulations in time. Besides, he says, they only chose to study aspects of the singularity that would not suffer from the limitations of the linearized equations. “We believe that when full nonlinear simulations are eventually done, our conclusions will prove to be robust,” he asserts.
Recall too that this study focuses only on a subset of singularities (outflying) in a subset of black holes (fast-spinning and supermassive). Spaghettification is still a very real threat when it comes to the more traditional Schwarzschild (non-rotating) black hole—but thanks to the laws of angular momentum, scientists don’t expect to find such simple objects outside of computer simulations. Instead, this work provides a new glimpse into the inner workings of a more realistic black hole.
And for all the Interstellar haters out there, it may be time to give the film a second chance.

–Eleanor Hook

*Burko adds, “A second common misconception is that at the boundary of a black hole the tidal forces are always so strong that they would spaghettify physical objects such as stars, spaceships, or astronauts. In fact, the more massive the black hole, the smaller the tidal force at its boundary. For a black hole as massive as Gargantua, the forces at the horizon are even smaller than on the surface of the Earth!” However, here we aren’t talking about an unperturbed, eternal black hole but one that interacts with matter and other object’s fields, making the entire situation much more complicated.


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