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A 'BKL singularity' is a non-symmetric, chaotic, vacuum solution to Einstein's field equations conjectured to represent the actual interior geometry of a "physical" black hole formed by gravitational collapse.
It is named after the three authors who first described it: V.A. Belinsky, I.M. Khalatnikov and E.M. Lifshitz.
The Mixmaster universe is a solution to general relativity that exhibits properties similar to those discussed by BKL.

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References

★ Колебательный режим приближения к особой точке в релятивистской космологии, Belinsky V A, Khalatnikov I M, and Lifshitz E M, , , Uspekhi Fizicheskikh Nauk (Успехи Физических Наук), 1970 English translation in Oscillatory Approach to a Singular Point in the Relativistic Cosmology, , , , Advances in Physics, 1970 .

★ Black Holes and Time Warps: Einstein's Outrageous Legacy, Thorne, K. S., , , W. W. Norton, 1994,