My quickest paper, and an unexpected collaboration

Some projects take a year. This one took about six weeks, and it wasn't even the problem I was supposed to be working on.

The object

In general relativity, a very heavy star that collapses under its own gravity usually forms a black hole, with an event horizon that hides everything inside. But some theoretical models, such as the JMN-1 spacetime, end in a naked singularity instead: an extremely dense core without a horizon. Studying what happens around such objects helps us ask whether everything we call a "black hole" really is one.

Real objects in space are rarely alone; they usually sit in magnetic fields. Those fields shape how charged particles move, and they play a big role in things we can actually observe, such as jets and bright glowing matter near the centre.

How it started

I was working on a different topic. In one of our research meetings, someone pointed out that the way I had defined the magnetic field around JMN-1 might have a flaw. That comment stuck with me, so I started digging.

Searching around, I found a paper by Mustapha Azreg-Aïnou that described a cleaner way to set up magnetic fields in this kind of spacetime. I used his method and managed to solve the first part of the problem myself. Then I did something I wasn't sure I should do: I emailed him, asked him to check whether my approach was right, and asked for his insight on a part involving Legendre polynomials (a family of functions that show up whenever you describe how something varies with angle around a sphere).

He replied, we started talking, and together we solved the problem in about three weeks. Within six weeks we had a draft ready for arXiv. It is probably the quickest project I have worked on.

What we found

In simple terms: JMN-1 is built by matching a region filled with matter to the empty space outside it. We found that part of the magnetic field jumps suddenly at that boundary, which means an electric current has to flow along the surface there. Yet when we looked at charged particles colliding near the boundary, the collision energy stayed smooth across it.

The paper was later published as JMN-1 singularity in weak magnetic field in the European Physical Journal C. The preprint is on arXiv.

The lesson I took from it: a critical comment is a gift, and a polite cold email to someone whose work you admire can go much further than you expect.