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Black holes form when massive stellar cores collapse catastrophically, creating a spacetime region bounded by the event horizon from which light cannot escape. The Schwarzschild radius (Rs = 2GM/c²) defines the event horizon size and is proportional to black hole mass. Near black holes, tidal forces become extreme and spacetime curvature dominates. Black holes are detected indirectly through accretion disk radiation, gravitational effects on nearby stars, and gravitational waves. Their interior remains causally disconnected from the observable universe.
From your study of post-main-sequence stellar evolution, you know that massive stars end their lives in catastrophic core collapse when nuclear fusion can no longer support them against gravity. For the most massive remnants — those exceeding roughly 3 solar masses — no known force can halt the collapse. The matter compresses without limit, and the resulting object warps spacetime so severely that it creates a region from which nothing, not even light, can escape. The boundary of this region is the event horizon.
The Schwarzschild radius Rs = 2GM/c² gives the size of the event horizon for a non-rotating, uncharged black hole. This formula connects directly to concepts from special relativity: c is the speed of light, the universal speed limit, and the event horizon is the surface where the escape velocity equals c. For a black hole with the mass of our Sun, the Schwarzschild radius is only about 3 kilometers — the entire solar mass compressed into a sphere smaller than a city. For the supermassive black hole at the center of the Milky Way (about 4 million solar masses), the event horizon is roughly 12 million kilometers, comparable to the size of Mercury's orbit.
The event horizon is not a physical surface — there is no wall or barrier an infalling observer would feel when crossing it. It is a causal boundary: the point of no return defined by the geometry of spacetime itself. An astronaut falling in would notice nothing special at the moment of crossing (for a sufficiently massive black hole where tidal forces at the horizon are gentle), but could never send a signal back to the outside universe. From the perspective of a distant observer, however, the infalling astronaut would appear to slow down, redden, and fade as gravitational time dilation stretches the light signals to ever-longer wavelengths — never quite seeming to reach the horizon.
Since black holes emit no light of their own, astronomers detect them through their gravitational influence on surrounding matter. Gas spiraling into a black hole forms a superheated accretion disk that radiates intensely in X-rays — some of the brightest X-ray sources in the sky are powered by stellar-mass black holes in binary systems. On larger scales, the orbits of stars near galactic centers reveal supermassive black holes: stars at the Milky Way's center trace elliptical paths around an invisible point mass. Most dramatically, gravitational wave detectors like LIGO have directly observed the spacetime ripples produced when two black holes merge, confirming predictions of general relativity and opening an entirely new observational window onto these objects.