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Wormholes are theoretical anomalies in the fabric of space-time. They link one set of co-ordinates in the universe with another. Nobody has seen a wormhole, but then again, nobody knows what they look like.
Black holes are collapsed stars, specifically, collapsed red giants. They are approximately the size of a Super Ball1, and one teaspoon would weigh several billion tons. It is believed that one or more black holes could form the very centre of our galaxy. They are only detectable because the particles of matter that form their accretion disks2 are constantly colliding with each other at velocities near the speed of light. This causes them to fuse into other types of matter, thereby releasing vast quantities of light, heat, and radiation which can be detected by very sensitive instruments on satellites orbiting the Earth.