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Newton described gravity as a force between masses. Einstein's general relativity says something deeper: mass and energy curve spacetime, and free-falling objects simply follow the straightest possible paths (geodesics) through that curved geometry. An orbit isn't a ball on a string – it is a straight line in a bent world. Turn on the Spacetime curvature grid to see a slice of that geometry (Flamm's paraboloid): the steep funnel is what “gravity” looks like near a black hole.
A particle moving sideways fast enough keeps “missing” the hole and orbits it. Far away this matches Newton, but close in, relativity adds new behaviour: there is a smallest stable circular orbit – the ISCO at 3 rs – and inside it matter spirals in no matter how it is launched.
The speed needed to climb out of a gravity well is v = √(2GM / r). At the event horizon it equals the speed of light, which is why nothing – not even light – can leave. Try launching a probe at 0.9 c from a small radius: it still falls back.
Matter uses the Paczyński–Wiita pseudo-potential Φ = −GM / (r − rs) which captures the key relativistic orbit features. Light obeys the exact Schwarzschild light-path equation. The ambient swarm loses energy to drag (a stand-in for viscosity) so it slowly spirals in, just like a real accretion flow.
The event horizon is the surface of no return. For a non-rotating black hole its radius is the Schwarzschild radius rs = 2GM / c² ≈ 2.95 km × (M / M☉). Squeeze the Sun to a 3 km ball and you would have a black hole; the horizon is not a material surface, just the place where escape would require faster-than-light travel.
Light can orbit the hole on an unstable circular path here. Slightly inward and it falls in; slightly outward and it flies away. Try the Photon ring preset.
The dark disc you see is bigger than the horizon. Light rays with impact parameter b < (3√3/2) rs ≈ 2.6 rs are captured, so the hole “blocks” a region 2.6× its radius across the sky.
A distant observer sees clocks near the hole run slow by √(1 − rs/r). Falling matter appears to dim, redden and freeze at the horizon – watch the particles fade as they approach it.
Nothing special happens locally when you cross the horizon – a falling observer feels nothing unusual there, but can never send a signal back out.
Light follows geodesics too, so a mass bends light passing near it. In weak fields the deflection angle is α = 4GM / (c² b) = 2 rs / b – exactly twice what Newtonian gravity predicts, a result famously confirmed during the 1919 solar eclipse. This simulator ray-traces every pixel through the Schwarzschild geometry, so you see real strong-field lensing:
Stars behind the hole are smeared and displaced; a thin Einstein ring forms where background light is bent all the way around.
The glowing arc over the top of the shadow is the far side of the accretion disk, bent over the hole by gravity. A fainter second image hugs the shadow – the photon ring.
Untick Gravitational lensing to switch to flat space: the sky is undistorted and the disk looks like a plain tilted ring.
Launch a Light beam to watch parallel photons get deflected: rays far from the hole barely bend, closer rays bend strongly, and those with impact parameter below 2.6 rs are swallowed.
Gas falling toward a black hole has angular momentum, so it flattens into an orbiting accretion disk. Friction between neighbouring rings heats the gas to millions of degrees; the inner edge, near the ISCO (3 rs), is the hottest and brightest. The disk stops there because no stable orbits exist further in.
The side of the disk moving toward you is brighter and bluer; the receding side is dimmer and redder. Gas moves at over half the speed of light near the inner edge.
Light climbing out of the gravity well loses energy, reddening the innermost regions.
The glowing specks are individual particles integrated in real time. Raise Accretion drag to make them spiral inward faster, and Mass to watch the horizon grow and swallow orbits that were safe a moment ago.