I attempted to build a real-time null geodesic integrator for visualizing photon paths around a non-rotating black hole. The implementation compiles to WebAssembly for browser execution with WebGL rendering.

Technical approach:

- Hamiltonian formulation of geodesic equations in Schwarzschild spacetime

- 4th-order Runge-Kutta integration with proximity-based adaptive stepping

- Analytical metric derivatives (no finite differencing)

- Constraint stabilization to maintain H=0 along null geodesics

- LRU cache for computed trajectories

The visualization shows how light bends around the event horizon (r=2M) and photon sphere (r=3M). Multiple color modes display termination status, gravitational redshift, constraint errors, and a lensing grid pattern.

Known limitations:

- Adaptive step sizing is heuristic-based rather than using formal error estimation

- Constraint stabilization uses momentum rescaling (works well but isn't symplectic)

- Single-threaded execution

- all geodesics computed sequentially

I am a cs major and so physics is not my main strength (I do enjoy math tho).. Making this was quite a pain honestly, but I was kinda alone in Christmas away from friends and family so I thought I would subject myself to the pain.

P.S I wanted to add workers and bloom but was not able to add it without breaking the project. So, if anyone can help me with that it would be much appreciated. Also, I am aware its quite laggy, I did try some optimizations but couldn't do much better than this.

Link to repo: https://github.com/shreshthkapai/schwarzschild.git

Have a great holidays, everyone!!