Four modules, one black hole
Curved spacetime, bent light, lensing, disk and jets—one module per step, scrubbable by visitors to any moment.
A science-center exhibit must make a passing visitor stop, understand and want to touch it again. Black holes are the hardest: the hole itself is invisible; what we see is what it does to light and spacetime. This lab draws one in code—mass pressing spacetime into a funnel, light bending and circling the photon sphere, a background galaxy stretched into arcs and an Einstein ring, and finally a lopsided accretion disk with jets.
Light paths are integrated from the Schwarzschild light equation and compared with the weak-field formula α = 4GM/(c²b); lensed images follow the lens equation; disk brightness includes gravitational redshift and Doppler boosting. Drag the mass, how close the light passes or the viewing angle, and the drawing, curves and readings change together. Your exhibit can be built the same way—as a touchscreen, projection or exhibit film.
10 solar masses · Schwarzschild radius 29.5 km · photon sphere 44.3 km · 1 kpc away · Einstein ring 9.0 mas
The grid is an embedding diagram of space around the hole: deeper toward the centre, with the horizon at the bottom. Colours and clocks show how fast time passes—slower near the horizon. Light has no mass but must follow curved spacetime, so it bends.
Far away the deflection is α = 4GM/(c²b); closer in, the exact angle grows far beyond the formula. Rays with b below 2.6 Schwarzschild radii are swallowed; those right at the edge circle the photon sphere at 1.5 radii several times before escaping.
Light from the galaxy passes on both sides of the hole, so one galaxy shows two images: the outer one stretched and brightened, the inner one squeezed and dimmed. When all three line up, the images join into a circle—the Einstein ring. This is the view magnified to milliarcseconds; the hole itself is far too small to see.
At the innermost stable orbit the gas moves at about half light speed; the side coming toward us is compressed, brighter and bluer, the receding side dimmer and redder—over ten times apart. Bent light lifts the far side of the disk above the shadow. Jets leave at 0.9c; seen nearly head-on, the counter-jet all but vanishes.
Curved spacetime, bent light, lensing, disk and jets—one module per step, scrubbable by visitors to any moment.
Light paths are integrated ray by ray; deflection, photon sphere, lensed images and disk brightness follow the equations, and curves, readings and drawing share the same numbers.
Mass, how close the light passes and the viewing angle are all draggable—ready for a gallery touchscreen that children and adults can explore.
The same lab becomes a touchscreen exhibit, dome or projection content, an exhibit film, or part of your website and guide app.
Science centers, museums, science associations, corporate showrooms
Interactive exhibits, touchscreen guides, science weeks
Where thrust comes from
Agriculture & foodHow to grow lettuce faster
Chemicals & materialsHot spot, pellets and coking
Construction & engineeringLoading, tensioning and cracking
Education & publishingPlanetary motion solved from Kepler’s equation
Energy & powerPeak shaving and valley filling
Environment & waterNitrogen and phosphorus removal
Geoscience, weather & disasterFrom warm-sea genesis to decay over land
Government science & industryStorm, infiltration and storage
Hospitals & health educationElectricity, valves and blood flow
Patents, legal & investmentPatent figures, ratios and claim chart
Medical devicesStenosis, dilation, deployment and apposition
New energy & batteriesHeat, cooling and thermal runaway
Pharma & biotechStructure, targeting, release and killing
Universities & research institutesTunnelling, feedback and atomic imaging
Semiconductors & electronicsFive steps to one circuit layer
Telecom & computingOne antenna array, many users at once
All13 step-by-step animations and uses across 18 client types
Listed here is what we’ve done and what people ask most. For other industries or uses, add us on WeChat and send a one-line brief—we’ll reply with an approach and quote within 1–2 working days.

Page updated 2026-10-24
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