As the black holes get closer, they emit gravitational waves, which are ripples in spacetime
These gravitational waves carry away energy and angular momentum, causing the black holes to spiral closer and closer together.
When the both black hole starts merging, their event horizons merge as well, and a single, larger event horizon is formed around the resulting a big black hole, bigger than the previous one (The supermassive black holes). The central singularities also merge in some way, but the exact nature of this process is not well understood due to the limitations of our current understanding of the fundamental physics at play near singularities
The process of merging of the two black holes approaching each other is known as black hole binary inspiral and merger.
It's important to note that our understanding of what happens near black hole singularities is based on theoretical models and calculations that rely on general relativity.
Second how do we know that two black holes will meet each other?
It is important to change this question slightly as: How do we know that two BH's meet in an else empty universe? This "else" is important.
What makes two small Blackholes different compared with two large stars of the same mass? (In an else empty universe)
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