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A really painful type of coordinate transformation I once had to develop to try and shed some insight on Hawking radiation near black holes.
Unfortunately the results were fucking ugly and I gave up trying to understand them, largely due to the fact that except under very specific circumstances they're basically impossible to calculate (you get something similar to divide by zero errors).
Nice case:
Not nice case:
There was a ton more related stuff I could have spent a PhD working on, but life didn't really allow it (and frankly I'm okay with that, I'm actually doing enjoyable stuff for the first time in my life instead of fighting my brain).
Are you a post-doc now? If so, congrats! If you dont mind me asking, what exactly was your research about (not a physics/mathy person so ELI5 would be appreciated)
Nah, I never even started a PhD mostly due to financial circumstances. But I've since realised I kinda hated academia because of untreated ADHD lol. I may go back to it one day after I've got treatment sorted but I really doubt it, I found my passion in music instead.
I'll try and ELI5 haha. Think of a black hole like a battery, stuff falls in to charge it and then it discharges by tickling empty space into creating particles. The problem is that the particles it creates seem to be random, which means it acts like a big delete button for the stuff that fell inside. Due to quantum stuff, this shouldn't be possible, so some process could exist to encode the information about the original stuff onto the particles that leave the black hole. Importantly this doesn't actually mean the particles that leave have to be the same as what fell in, you just need to able to look at them and then reconstruct it. Kinda like if you scrambled a book in a way which makes it look random, but is actually a secret code that still has the whole story contained inside.
My research was to look for that information being written on the particles leaving the black hole, basically by comparing how space and time outside the black hole changes over time and seeing what it does to the tickling.
Holy shit that's insanely cool actually. But yea academia does get kinda ridiculous sometimes, I'm glad you found your passion for music instead!
Assuming you meant ticking , but that is a great insight and perspective to research from!
Nah, I absolutely meant tickling. Black holes make empty space wiggle a bit and it produces particles.
The actual process is much more complicated ofc but that's the picture in my head of the quantum field theory, if you tickle the surface of a still pond it'll make ripples which is sorta the same thing.