The characteristics of a star that make it most likely to become a black hole primarily include:
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Mass: The most critical factor is the mass of the star. Stars with an initial mass of about 20 times the mass of the Sun or greater have the potential to end their lives as black holes. Once they exhaust their nuclear fuel, they may undergo a supernova explosion, leaving behind a black hole.
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End Stage Evolution: Stars that can undergo supernova explosions (those that fuse elements up to iron in their cores) are more likely to leave behind a black hole. In contrast, less massive stars typically end up as white dwarfs or neutron stars.
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Metallicity: The metallicity (the abundance of elements heavier than hydrogen and helium) of the star can also play a role in its evolution. Massive stars with higher metallicity may lose more mass through stellar winds, affecting their final remnants.
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Rotation: A rapidly rotating star may influence its collapse and the formation of a black hole. The specifics of how angular momentum is conserved during the collapse can lead to the formation of a rotating black hole (Kerr black hole).
Overall, the most pivotal characteristic is the star's mass; it is the determinant that primarily dictates whether it will become a black hole after its life cycle.