Zihan Yan

Looks super interesting! Will apply!

Generalised focusing theorem and dynamical horizon entropy in diffeomorphism-invariant theories I summarise recent progress on light-ray focusing and horizon thermodynamics in general diffeomorphism-invariant theories of gravity coupled to bosonic matter. In pure gravity and with scalar or vecto...

That’s the story! If you’re curious about generalised focusing, entropy, or horizon dynamics—let’s discuss!
Full paper: arxiv.org/abs/2509.00628 (8/8)

Next steps: extend these results to semiclassical & nonlinear regimes.
Excited to see how “entropic geometry” reshapes our view of spacetime & gravity. (7/8)

For higher-spin fields, the theorem holds conditionally. I propose a “higher-spin focusing condition” as a criterion for physical consistency. (E.g. 3D sl(3,R) higher-spin black holes satisfy it ✅) (6/8)

Key insight: Geometrically, light rays don’t always focus under positive energy in general gravity theories. But in entropic geometry—measuring separation via Wall entropy, not area—they do. Gravity remains attractive! (5/8)

This generalised expansion decreases monotonically under the null energy condition. Even more: it equals the change in Wall entropy density, which satisfies the 1st & 2nd laws. So it’s a natural higher-order/dynamical generalisation of BH/Wald entropy. (4/8)

We extend this to all diffeo-invariant gravities with bosonic matter.
On perturbed Killing horizons, the linearised equation of motion gives a generalised Raychaudhuri equation → a notion of “generalised expansion.” (3/8)

In GR, the focusing theorem says: with positive energy (NEC), light rays converge. This simple idea reveals the attractive nature of gravity, and underpins Hawking’s area theorem & Penrose’s singularity theorem. (2/8)

🚀 My first conference paper is out!
arxiv.org/abs/2509.00628
Based on my GR24 talk, it summarises 2 years of work with my supervisor Aron Wall on generalised focusing theorems & horizon thermodynamics in diffeo-invariant gravity. A short thread 👇(1/8)

Happy New Year! 新年快乐！All the best to our 2025!

I hope I can grow a better vision for theoretical physics in the new year… I always feel I’m so naïve…

It was fun to explore the intricacies of higher-spin fields from the perspectives of gravitational focusing and horizon thermodynamics. There are so many open questions to address in the future…

arxiv.org/abs/2412.07107

Wow this is super useful!

New departmental cat of DAMTP, Cambridge

Just noticed I was already on Bluesky way before I joined 😂😂😂

Thanks very much!

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Hi! I’m new here! Glad to chat about black holes and quantum gravity or anything about physics and mathematics!