Researcher backs up Einstein’s theory with math

Wouldn’t it be able to stay straight up if you used your hand to move it around and keep it balanced?

It’s different, because then you would be adding a lot of momentum to the pendulum to keep it balanced in that vertical position.

The idea of ​​stability is crucial in physical and mathematical objects such as the pendulum, because the difference between being stable and unstable is the difference between something that is doable and not doable. It is impossible to find the pendulum in this upward position. Because in fact, we never manage to position the pendulum exactly upwards, because we will always have a positioning error. It can only be posed in our mind as a balancing point, but not in the real world.

And how does this connect to black holes?

Black holes are solutions to Einstein’s equation, and they are the balance point of Einstein’s equation. Kerr’s solution appeared in 1963, several years after Einstein’s equation was written in 1915. This solution finds a balance point with Einstein’s equation which does not change over time. But then the question is: is it a downward pendulum or an upward pendulum? Because if it’s a pendulum pointing up, then that’s a good solution, but it can’t represent anything in the real world.

The physics community has done stability analysis for these solutions of black holes in certain simplified contexts and found no signs of instability, so they have inferred that black holes are stable, without actually proving it. But it took the math community about 60 years to catch up and figure out what the real mechanism was.

Could we have assumed that black holes were stable just by looking at them and observing that they exist?

That’s a very good question, but observing black holes isn’t as simple as, you know, observing a cat. The way images of a black hole are produced is that there is an image captured by telescopes, but there is also a plan that uses Kerr’s solution. How do you interpret the data you see? By comparing it with your model. Some things are inferred by observation and others are assumed based on mathematics.

Have you always been interested in space? Or did you come here because the phenomena in outer space posed the most interesting mathematical problems?

I studied mathematics in license when I was in Pisa in Italy, then I did a master’s degree in mathematical physics in France. Since high school or even before, I’ve always loved math and physics, so I was looking for something that would bring them closer together.

And then, of course, black holes: who doesn’t think they’re fascinating?

The month I started a PhD, which was September 2015, was when the first observation of gravitational waves from LIGO occurred. It was announced in February 2016. [That year, two observatories in Louisiana and Washington known as LIGO detected gravitational waves, ripples in space-time that Einstein’s theory predicted would occur, proving the veracity of his predictions.]

I was here. I was a student at Columbia and I remember going to Lerner Hall, they projected the discovery of gravitational waves in February 2016. It was so exciting. Maybe it was some kind of fate. This sighting gave the field a big boost, making it much richer than if you didn’t have those sightings. Some other areas of physics, like string theory, don’t have these kinds of waves of data from real observations.

What brought you to Columbia in particular?

I did my master’s in France, so I was already abroad in a way. And I wanted to go somewhere else. I always wanted to have an experience in the United States, for example. I applied for doctorates very widely. And I had a few offers of admission and then I visited Columbia and was in New York. It was very hard to say no, it was so exciting. They made me visit the department and being in town, with other students, I was very quickly convinced. Also because of the people here working on differential geometry and general relativity, Columbia made a lot of sense.

Do you have the impression that you are following developments at NASA and other space agencies very closely?

Not really. On a personal level, I love it, of course; I receive all newsletters. But these are not directly related to the work I do. I am not a great astronomer.

The field of mathematics is very masculine. Did you have strong female mentors coming into the field? Do you see this as a role you would like to play for young female mathematicians?

Mathematics tends to be very male dominated. Just to give an example, our department has only four full professors out of 29, and there are other departments across the country where the ratio is even worse. I believe it is very important to have mentors that you can relate to as it helps nurture a sense of belonging when you are a student. I was fortunate to have been exposed to amazing academics during my graduate years at Columbia who showed me different ways to be a mathematician. For my part, I can only hope to have a positive impact on young people passionate about mathematics and physics, and I do my best to make them feel like they belong in this field. Because they do.

What do you miss the most at home, in the kitchen?

What I miss the most is ice cream, gelato. Here you can find some, but it’s downtown, or downtown, and very expensive. But for pizza, I think I can find even better pizza here than in Italy.

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