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Mathematician Takes Journey to Black Hole

Published: October 24, 2017
Emilio Toro, associate professor of mathematics, takes a closer look at one of the universe’s most enigmatic phenomena.
Emilio Toro, associate professor of mathematics, takes a closer look at one of the universe’s most enigmatic phenomena.

»This story appeared in the Fall 2017 UT Journal.

Among the quarks, quasars, pulsars and other improbable objects of our universe, perhaps one stands out for being at once utterly bizarre and yet familiar enough that its name has entered our lexicon, at the root of many common metaphors.

That is the black hole.

They are potentially huge — the mass of billions of suns. Yet their “diameter” is infinitely small. They are invisible. Yet we know they exist by theory and the effect they have on the celestial bodies around them.

Perhaps what is oddest about them — to a layperson, at least — is that mass and energy can pour into them never to exit, in effect vanishing from the universe.

“I suspect that people found that idea rather fascinating,” says Emilio Toro, associate professor of mathematics. “How could it be that things go inside this mysterious object and they disappear? I think the notion that things can go in and never come out, they just go away forever, has taken hold of the imagination.”

But they are even more surprising than that.

Toro, in addition to teaching higher mathematics, also lectures on cosmology, space and time and the general theory of relativity. Fascinated by black holes and how their gravity bends the space-time fabric of the universe, he pulled together a PowerPoint presentation and delivered a lecture to his astronomy club in his native Colombia. Back home in Tampa, he translated the lecture and presented it to a general audience of faculty, staff and students at UT in February.

These were “students with very different backgrounds,” says Toro. “I designed the lecture so it wouldn’t be too heavy on the math part, because I knew as soon as I started putting equations on the board, people would get frightened or just turn around and leave the classroom.”

To make the subject as accessible as possible, he framed the talk as “A Journey to a Black Hole.” Anna, the adventurous astronaut, takes the trip, while Patricia, the prudent one, merely observes.

“One is going to go into a black hole and the other one is going to stay outside, safely away from the black hole,” says Toro. “The basic question of the lecture was: What are both of them going to see? Are they going to see the same thing happening? Or are they going to see different things? That’s why we needed two people.”

And that is the nut of the lecture: Because of the strange warpage of time and space by the immense gravity of a black hole, the two hypothetical participants observe two very different events. “There is not one reality,” says Toro. “That is the point of the lecture — that essentially there are two realities.”

But first, what is a black hole?

Astronomers and thinkers as long ago as the late 1700s, including Pierre-Simon Laplace, conjectured that objects might exist in the universe whose gravitational fields were so strong even light could not escape. But it was not until Albert Einstein’s publication of the general theory of relativity in 1915 that the theoretical groundwork was laid for really understanding such phenomena. A year later, German physicist and astronomer Karl Schwarzschild described the mathematics of such an object. Interestingly, Einstein himself could not accept the idea of such an odd thing. “Even Einstein was opposed to the existence of black holes,” says Toro. “He didn’t believe that they could exist.”

But astronomers came around to the idea, and in 1960 American physicist John Wheeler coined the term familiar to everyone now — black hole. The first observational evidence of black holes began trickling in a decade later.

To function as a black hole, an object must be dense beyond anything we have experienced directly. For example, if Earth, in all its mass, were compressed to the size of a large marble, its gravitational force would be great enough to keep light from leaving, creating a small black hole. Others, such as the black hole at the center of our own Milky Way galaxy, have been calculated to be 4.3 million times the mass of our sun (and more than a trillion times the mass of Earth).

Black holes can form when one star steals matter from another one, says Toro. If a star grows too large, gravity will compress it into a black hole.

Such an intense gravitational field creates an “event horizon,” a spherical zone around the black hole sometimes called the “point of no return.” Anything, even light, crossing the event horizon cannot move fast enough to escape. The event horizon of the largest known black holes is roughly the size of our solar system.

“I don’t think within the scientific community there are people who would question the existence of black holes,” says Toro. But it’s not as though all the science is settled. Physicists as eminent as Stephen Hawking, the English theoretical physicist at the University of Cambridge, have postulated that “information” leaks from black holes in the form of “Hawking radiation.”

But back to Anna and Patricia. As Toro imagines their experience, Anna is in a spacecraft, hurtling toward the black hole. Patricia is somewhere at a safe distance, far from the event horizon, peering through a telescope.

Anna and Patricia each have a flashlight and a “clock,” made of a particle of light bouncing endlessly between two mirrors. As the two women part ways, the beam from each flashlight appears white — to themselves and to each other. And their light beam clocks are running in sync.

As Anna approaches the event horizon at rapidly increasing speed, she looks at her flashlight and sees white light. Her clock is still ticking (if light could tick) normally. But Patricia sees something quite different. Patricia sees Anna’s flashlight beam shifting toward the red end of the spectrum. “It’s called the relativistic redshift, and it is caused by the gravity in the vicinity of the black hole,” says Toro.

And Anna’s clock grows slower. As her speed increases toward the speed of light, the particle of light has to travel not only the distance between mirrors but also a significant distance forward. As the light beam has to travel farther, the cycle from mirror to mirror slows down. In fact, Anna’s progress seems to slow infinitely. As Anna’s flashlight grows redder and dimmer, as her clock slows, from Patricia’s perspective, she never crosses the event horizon.

As Patricia notices these changes, Anna sees that nothing has changed. She hurtles across the event horizon toward oblivion, her light white and her clock ticking. The differential in gravity stretches her like spaghetti before she is crushed at the core of the black hole.

“Patricia sees Anna dropping into the black hole forever. She is always approaching. From Patricia’s perspective, Anna never crosses the event horizon. She just approaches and approaches and time slows down. If Patricia came back 20 years from now to see what’s going on, she would still see Anna falling into the black hole. Anna on the other hand crosses the event horizon, and once she crosses the event horizon, she is gone from the known universe,” says Toro.

“That is the end of the trip, and that is the end of the lecture,” he says. Because nothing, not even light, can escape from inside the event horizon, there is no way to signal what might have become of Anna. “Anna cannot send a message saying, ‘I just crossed the event horizon,’” Toro says.

“Patricia goes back to earth and tells people that she saw Anna falling into the black hole, and that’s the only thing that Patricia can report truthfully,” says Toro. “On the other hand, Anna is gone into the black hole and that is the end of that.”

Toro found that as he gave his black hole lecture first in his native Spanish, he struggled with the technical jargon, which he had learned in English during his 30 years at UT.

“The words in Spanish sometimes escaped me,” he recalls. “So sometimes the members of the audience would jump up and say, ‘Oh, this is what you’re trying to say.’ Oh, yes, thank you.”

Toro says he devised the lecture as an advertisement for science, especially in an age where science is viewed by some as just another social narrative that can be molded, interpreted and contravened by personal experience. He wanted students to appreciate the excitement of discovery.

“Science can be interesting, it can be fun, it can be accessible,” says Toro. “It produces surprising results, things that go very much against our common sense.”

Story by Greg Breining

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