He did not discover them. He did some calculations that predicted the possibility of the existence of black holes.
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Karl Schwarzschild discovered the first exact solution to Einstein's field equations of general relativity, now known as the Schwarzschild metric. This solution describes the gravitational field outside a spherically symmetric non-rotating mass, such as a black hole.
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No, Albert Einstein did not specifically discover black holes. His theory of general relativity laid the foundation for understanding the structure of spacetime, which contributed to our understanding of black holes when other scientists like Karl Schwarzschild and John Wheeler applied his principles to describe them.
The Schwarzschild radius is directly proportional to the mass of the black hole. It is about 2.95 km for every solar mass.
Black holes neither expand nor collapse in the conventional sense. Once a black hole forms, it remains the same size unless it gains mass by absorbing matter or energy. However, black holes can grow in size over time as they capture surrounding material.