Schwarzschild Radius and Event Horizon

The Schwarzschild radius is the radius at which any mass has an escape velocity equal to the speed of light. It is calculated as twice the product of the gravitational constant and the object's mass divided by the square of light's speed. This critical radius determines whether an object becomes a black hole.

Escape velocity increases as an object's radius decreases while its mass remains constant. For example, if the Sun's radius were halved, escape velocity would increase from 618 km/s to 873 km/s. This relationship shows that compressing mass into a smaller volume dramatically increases the velocity needed to escape its gravitational pull.

An event horizon is the spherical surface surrounding a black hole located at the Schwarzschild radius. Inside this boundary, escape velocity exceeds the speed of light, making escape impossible. Any object with a radius smaller than its Schwarzschild radius becomes a black hole surrounded by this event horizon.

Light cannot escape a black hole because the escape velocity inside the event horizon exceeds the speed of light, which is the maximum speed at which any object can travel. Since nothing can travel faster than light, not even light itself can overcome the black hole's gravitational pull and reach the outside universe.

When an object becomes sufficiently dense, it collapses upon itself and forms a black hole surrounded by an event horizon. The term black hole, coined by astronomer John Wheeler in 1969, refers to objects from which nothing can escape. Karl Schwarzschild first identified this phenomenon mathematically in 1916.

Although black holes cannot be directly observed because light does not escape their event horizons, astronomers detect them through overwhelming indirect evidence. Their effects on nearby stars and infalling matter are typically interpreted by making astronomical observations of radiation and gravitational influences on surrounding objects.

Escape velocity depends on an object's mass and radius. When escape velocity equals the speed of light, the object reaches its Schwarzschild radius. This relationship between space-time curvature and the general theory of relativity explains why extremely dense objects create regions from which nothing can escape.