Gravitational Wave Astronomy

Today we are going to talk about gravitational wave, this is an exciting new window to observe the universe. Let’s get started. So if you remember Einstein’s field equation was like this. So, matter on the right side tells space how to curve, and then space tells matter how to move. So Einstein connected these two, space and matter, equal. And if you think, if you think about the equation, if the matter changes, if the gravitational field changes, then that’s gonna change the space curvature. But, Einstein general relativity also told us that speed of the light is the fastest thing the information can move.

So, in, if matter changes, gravitational field changes to affect the space curvature, it can only affect at the speed of the light, cannot be much faster. This is a big difference from Newton’s gravity. In Newton’s gravity this change, or gravity, is gonna be instant. But Einstein said no, no, it’s not instant it’s a speed at the speed of light. So in this sense if matter changes the gravitational field, then there will be a time or wave to change the space curvature, so this is the gravitational wave. Um, so as an equation matter tells space how to curve, and in this kind of stationary state it’s fine, this space is curved by the gravity of the earth, right?

But on the other hand in case of something like this, so this is an example of two black hole mergers, and then when black hole merging, these two are rotating each other, and changing the gravitational field constantly. In this case the curvature of the space also changes instant, changes, um, instantly, but to carry this wave to outside, it only proceed(s) with the speed of the light. This is the so-called gravitational wave. So this is the animation, again, two black holes are merging, about to merge, they’re rotating each other, and the gravitational field is changing because of this rotation, and this change is moving outwards as a gravitational wave, so these ripples here are all gravitational wave(s).

And then finally two black holes merge into one black hole and it is the biggest wave of the gravitational wave going outward. Okay, so then how can we detect this gravitational wave predicted by the Einstein equation? A gravitational wave is gonna move, stretch the space, uh, stretch or shrink the space just like this cartoon here. But this stretching amplitude, “h,” is a fraction of stretching or squeezing here, in this animation it’s 50 percent squeezing “h” = 0.5. But in case of real gravitational wave, this amplitude is 10 to the minus 21. This is very, very small number.

So that when gravitational wave comes, the ice is stretched or squeezed or stretched a little bit like this, but this animation is exaggeration. Actually it’s only one thousandth of the size of the proton that changes, in case of the, um, LIGO detector which I mention later. Proton is a fundamental particle. It’s very, very small, 10 to the minus 18 kilometer, and one thousandth of the size of the proton is the change. So this is a very, very difficult observation. So how do we measure it? So, America has this LIGO gravitational wave detector, this is one of them their arms here. How does this work is, here’s how it works. It’s a laser interferometer.

Um, here, um, from the source you shoot the laser and in this mirror is going to split the light into two. And there’s a mirror on both sides and the mirror is gonna, um, reflect the light and the light comes back and they get together here again. And if there’s no change this distance is the same. So if there’s no gravitational wave the distance is the same so light gets together and then goes back to the detector. But, if it is a gravitational wave on one side, this side, the distance is stretched or squeezed, the distance changes.

So, when the light comes back and gets together again here, there’s a shift, because now the distance here, and distance here are a little bit different. So there the lights will interfere and then we can observe interference at the detector. So this is how we detect the gravitational wave. This is one of the off arm, arms of the LIGO gravitational wave detector this one arm is four kilometers long, inside this pipe. An expected signal would look like this.

When two black holes merge there will be a gravitational wave of larger frequency, and then as the black holes merge, um, they get closer and closer, to frequencies get higher and higher, and then finally the biggest gravitational waves come when they merge into one, and then once they become a, become one, the signal disappears. So this is theoretically expected signal. And in September 14th 2015, this is just a week after LIGO started a test run, this is even a test run they detected this signal.

LIGO has two detectors in Humboldt and Livingston, and they detect exactly the same signal, so this is a signal, you see, this is compared to theoretical curve this is exactly expected from the merging of two black holes, and the same signal is also detected in the Livingston. So this is the first detection of the gravitational wave. And if you analyze this frequency, um, you can tell this is a merging of 35 solar mass black holes, 30 solar mass black holes merges into 162 solar mass black holes. And as you notice these two, sum up of these two doesn’t match this 62, right?

This, if you add these two its 65, so three solar mass of the mass was lost, as a gravitational wave, it’s emitted as a gravitational wave. So gravitational wave is detected, and this is in multiple sense, it’s a, it was a breakthrough. First, it’s a first direct detection of a gravitational wave, so that Einstein’s prediction was correct. And also, this is the first time we directly observed a black hole merger, we never witnessed the black hole merges. And also, this is the first detection of intermediate mass black holes, 30 solar mass and 60 solar mass. We knew these kind of exists, black holes, we guessed these kind of black holes exist, but we never detected observationally.

This is the first time. And most importantly, this is the opening of a new window to see, to observe the universe. Up to now, we’re using telescopes and electromagnetic light to observe the universe. But gravitational wave is not a light, this is completely new way to look at the universe. So this is the moment, almost as big as Galileo Galilee invented the telescope, and we had a new window, new way to look at the universe. And this is why the gravitational detection, uh, got the Nobel Prize, the Nobel Physics Prize in 2017.

And then gravitational wave detectors are still working, and upgrading, becoming more and more sensitive, and more exciting measurement of gravitational waves are coming in the, our near future. So we live in a very, very exciting moment.