Made after discovering a neat method of calculating Thomas precession, it blossomed into a full description of all 2-dimensional surfaces of constant curvature, both Riemannian and Lorentzian.

Of particular interest is a clever method of generating geodesics, and a derivation of a Penrose diagrams suitable for people without any differential geometry tools -- which are revealed to be a simple hyperbolic Mercator projection for surfaces of constant curvature.

status: arxiv, in revision for American Journal of Physics; link

This one got made during a conference. I got an idea for novel geometric proofs of classic special relativity results -- the relativistic rocket equation and the relativistic Doppler effect.

The proofs use phase space Minkowski diagram to illustrate the results, and hyperbolic trigonometry to translate the visual to the language of algebra. In particular, the Doppler effect proof simultaneously shows every single Doppler related effect as well as the searchlight effect, in a few simple diagrams. See also arxiv.

status: American Journal of Physics 93, 633–642 (2025); link

A thorough paper on what happens when you fall beyond the event horizon of a Schwarzschild black hole. Inspired by an inconsistency in a few books; most prominently Spacetime and Geometry by Sean Carroll: it turns out squirming is better than staying still, which you naively would expect to be the best possible outcome for maximising proper time!

It's my first big paper. Started the trend of me getting sidetracked by random ideas. But at least the paper is quite interesting, and I've obtained some new results, such as the exact expression for the longest possible time taken on an accelerated worldline between the event horizon and the singularity. For the black hole big boys, even accelerations achievable by current technology can help!

status: arxiv, ACCEPTED to Acta Physica Polonica B; link