Indexing the archive…
Your Universe of Digital Possibilities
A mass doesn’t pull on light — it curves the space the light travels through, and the beam, going perfectly straight, bends anyway. Drag the mass across the starfield: a star sliding behind it stretches into a ring of its own light, the photon ring flares, and the event horizon cuts a black hole in the sky. The same effect lets us weigh galaxies and see what hides behind them.
Matter tells spacetime how to curve; the curvature tells matter (and light) how to move. Gravity isn’t a force in the picture at all.
A ray grazing a mass bends by this angle — exactly twicethe Newtonian guess. Eddington’s eclipse confirmed it and made Einstein famous overnight.
Solve for the apparent position θ given the true source β. When the source sits dead behind the mass, every solution is a circle — a full ring of radius θE. (This is the line the shader inverts per pixel.)
Clocks deeper in the well tick slower (the −(1−rs/r) term). The event horizon is at rs = 2GM/c², where the escape speed reaches light.
This is not an abstraction you can ignore: your phone’s GPSwould drift kilometres a day if it didn’t correct for clocks running faster in orbit’s weaker gravity (~38 µs/day). The same lensing you’re bending here lets astronomers weigh invisible dark matter and use whole galaxy clusters as telescopes to see the early universe — and in 2019 it let us photograph the shadow of a black hole. Straight lines, in curved space, do all of this.