A black hole is a region in space where gravity is extremely strong, and nothing, not even light, can escape its gravitational pull. It is formed when a massive star collapses under its own gravitational force at the end of its life cycle. The collapse results in an extremely dense and compact object with a gravitational field so intense that it creates a region of spacetime from which nothing can escape, known as an event horizon.
The size of a black hole is typically described by its Schwarzschild radius, which is the radius of the event horizon. It is directly proportional to the mass of the black hole. The formula for the Schwarzschild radius is given by:
r = 2GM/c^2
Where:
- r is the Schwarzschild radius,
- G is the gravitational constant,
- M is the mass of the black hole, and
- c is the speed of light in a vacuum.
This formula tells us that as the mass of a black hole increases, its Schwarzschild radius, and therefore its size, also increases. Black holes can range in size from a few times the mass of our Sun to supermassive black holes found at the centers of galaxies, which can have masses billions of times that of the Sun.
The formation of a black hole is caused by the collapse of a massive star. When a massive star runs out of nuclear fuel, it is no longer able to sustain the outward pressure generated by nuclear fusion in its core. The force of gravity then takes over, causing the star to collapse inward. If the star is sufficiently massive, the collapse continues until it becomes a black hole.
The collapse process is driven by the star's own gravity, which compresses the stellar material to extremely high densities. As the star collapses, its core becomes a singularity, a point of infinite density and infinitesimal size, surrounded by the event horizon that defines the black hole's boundary. Our current understanding of physics breaks down at the singularity, and it is an area of active research in the field of theoretical physics.