A Singular Family

This week, I got some great questions from my nephew Ezra, along with his parents Nate and Carrie. I gave them some quick answers off the top of my head, but I thought they deserved a more in-depth treatment as well.

Ezra: What does a gravity wave feel like [to a person]?
As a reminder, gravitational waves warp space as they pass. If a wave passed through the center of a hula-hoop, it might look like this:

Each image is a point in time. Adapted from my thesis.

Gravitational waves are incredibly weak, which is why we need 2.5 miles of detector to pick them up. They’re a squeezing and stretching of space, so if you could feel them, they’d be a combination of a hug (awww) and a medieval rack (ahhh!). Some of the early detectors were big pieces of tuned metal that scientists hoped would ring like a xylophone if the correct frequency passed by. Those were never sensitive enough though.

Nate: But aren't they weak because they're distant? What if you were closer to a pair of black holes approaching collision? Could you be close enough to feel the waves but far enough to not be inside?

Good point! We can take the first LIGO detection, GW150914, as an example. According to that paper, the distance was about 410 megaparsecs, and the peak strain was 10^-21. Strain is the fraction by which the wave changes distances, so a meter stick would be stretched and squeezed by 1/1000000000000000000000 meter! That's pretty tiny, but strain drops off as 1/distance, so we can get a bigger effect closer to the collision. We probably don't want to be inside the event horizon of the final black hole, which has a radius of

Plugging in the 62 solar masses from the paper, we get 183 km. Supposing a 6 ft person observed the collision from 200 km away then, their height would change by a little over 4.5 inches!

Carrie: Is a black hole a hole in space-time or a depression?

It's both! -ish. This is a difficult question to answer, since the whole point of a black hole is that we don't know what's going on inside it. The trouble is that when a star collapses into a black hole, it creates a singularity – a point of infinite density. That creates a lot of problems for General Relativity, since things falling into the singularity could wind up going faster than light, and other bad things that happen when you have an infinite quantity. Instead, we put an event horizon around the singularity at the point where light can no longer escape from it, which is usually where bad stuff starts. Wikipedia has some nice representations of a singularity with and without an event horizon (bad stuff not included):

Black hole, via Wikimedia Commons

Naked singularity, via Wikimedia Commons

Thanks for some great questions!