Black holes do not die simply because there are too many of them in an area. The dynamics of black holes and their interactions are governed by the laws of general relativity. However, there are a couple of ways to consider the implications of having many black holes in a region:
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Gravitational Interactions: If there are many black holes in proximity, they can interact gravitationally, which sometimes leads to the merging of black holes. This would not cause a black hole to "die" in terms of disappearing but rather result in the formation of a larger black hole.
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Radiation Emission: One way a black hole can lose mass is through Hawking radiation, but this process occurs very slowly for massive black holes and is generally not influenced by the presence of other black holes.
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Accretion and Growth: Black holes can gain mass by accreting matter. If many black holes are surrounded by a lot of gas and dust, they may actually grow rather than die. In scenarios where multiple black holes absorb nearby material, it can lead to a significant increase in their mass.
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Eventual Cooling and Star Formation: In the long term, over astronomical timescales, the universe is expected to evolve in such a way that most stellar material will be converted into black holes, and as stellar formation ceases, cosmic activity will decline. However, this process is unrelated to the presence of many black holes.
In summary, while an increased number of black holes can lead to certain interactions such as mergers, it doesn't directly lead to the "death" of black holes. Their fates are primarily dictated by their own physical processes and the dynamics of the surrounding environment.