Final answer:
The Schwarzschild radius, or event horizon radius, of a black hole is directly proportional to its mass, following the equation Rs = 2GM/c². This relationship allows us to determine the size of a black hole's event horizon by knowing its mass, with a practical example being that the radius is about 3 km per solar mass unit. The event horizon defines the point beyond which escape is impossible, with a central singularity inside.
Step-by-step explanation:
The mass of a Schwarzschild black hole is directly related to the radius of its event horizon. According to the theory of General Relativity, the Schwarzschild radius (Rs) can be calculated using the formula Rs = 2GM/c², where G is the universal gravitational constant, M is the mass of the black hole, and c is the speed of light. This relationship implies that as the mass of the black hole increases, the size of the event horizon also increases proportionally.
If we consider a black hole with a mass that is a multiple of the Sun's mass, we can express the Schwarzschild radius in practical terms. For a black hole with mass M times that of the Sun, the event horizon radius is roughly 3 km times M. This simplifies calculations significantly for black holes of various masses in relation to the Sun's mass.
The event horizon, or Schwarzschild radius, marks the boundary of a black hole. Beyond this radius, not even light can escape the immense gravitational pull of the black hole, rendering it invisible to direct observation. At the center of the black hole is a singularity, a point of infinite density and zero volume, where matter that falls into the black hole is thought to accumulate.