To date observations have not yet unequivocally determined whether the universe is open or closed. Although for the luminous matter Ω≲0.1, the possibility of existence of non-luminous matter (especially if the neutrino has a non-zero mass) leaves ground for considering that the universe may indeed be closed. In this case the universe is expected to recollapse and become again, at a time to, radiation dominated. Hence R(t) ∼ (tf−t)1/2 ∼ 1/T (t), where tf is the time of collapse to the singularity and T is the temperature. During this new radiation dominated era, a black hole of mass Mo will accrete at a rate

where ρ(t) ⋍ αT4 (t) and r(t) = 2GM(t)/c2. Eq (1) upon integration yields

(All subscript zero quantities are taken at t = to). Eq (2) shows that the mass of the black hole diverges when τo/τ ∼ Mo/4πro2 ρo cρo where τo = tf − to.