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In this paper $4$ dimensional Riemannian (or Euclidean) vacuum general relativity is recovered from a phase transition by spontaneous symmetry breaking within a quantum field theory (all in the sense of the algebraic approach) provided by the unique II₁ hyperfinite factor von Neumann algebra. The formal temperature of this phase transition is T=1/2TPlanck≈7.06× 10³¹ K.
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Gábor Etesi (2024) studied this question.
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