Relativistic Geodesic & Gravitational Lensing Simulator

General Relativity 2D
Model Mass Parameter: 1000 M☉
Schwarzschild Radius (Rs): 60 px
Photon Sphere (1.5 Rs): 90 px
Active Particle Mode: Light Ray (Photon)
Controls:
Mode:

Read the trajectories as a heuristic model

What is simulated here, and what does the photon-sphere guide mean?

This workspace advances Cartesian position and velocity using a Newtonian attraction plus an angular-momentum correction. It is a visual heuristic, not a validated spacetime geodesic solver. Compare its controls and trails without interpreting the telemetry as a measured relativistic prediction.

Light and massive particles share the same acceleration update. No metric, null constraint, physical pixel scale or convergence evidence is supplied. Five fixed substeps run per frame, so browser frame cadence affects displayed evolution.

Try a worked example

The drawn photon-sphere guide is 1.5 times the horizon radius: a 60-pixel horizon gives a 90-pixel guide. This is the Schwarzschild radius ratio, not evidence that this integrator produces a correct circular light orbit. For direction changes, initial 179° and current −179° differ by 2° on a circle, not 358°; the corrected display takes the shortest angular difference.

Separate guides from termination rules

For the nonrotating Schwarzschild geometry, the photon sphere is at 1.5 horizon radii. NASA’s visualization explains that geometry; it does not validate this page’s update equations. NASA: visual distortions near a black hole

This program marks capture at 0.95 times its drawn radius and marks exit beyond 1,500 pixels. Those are numerical termination rules. A finite screen boundary cannot prove escape to infinity. Mass and constants are internal visual parameters rather than a documented conversion to solar masses and physical time.

Interpret closest-approach telemetry cautiously

The angle-change display compares consecutive new record closest-approach samples, not successive orbital periapses. Its global history can mix multiple particles. It therefore cannot establish precession per orbit. The deflection display is an instantaneous heading change from launch, not necessarily a far-field scattering angle.

Sources and further reading
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