Mass of the universe in a black hole

Abstract

If spacetime torsion couples to the intrinsic spin of matter according to the Einstein-Cartan-Sciama-Kibble theory of gravity, then the resulting gravitational repulsion at supranuclear densities prevents the formation of singularities in black holes. Consequently, the interior of every black hole becomes a new universe that expands from a nonsingular bounce. We consider gravitational collapse of fermionic spin-fluid matter with the stiff equation of state in a stellar black hole. Such a collapse increases the mass of the matter, which occurs through the Parker-Zel'dovich-Starobinskii quantum particle production in strong, anisotropic gravitational fields. The subsequent pair annihilation changes the stiff matter into an ultrarelativistic fluid. We show that the universe in a black hole of mass $M_\textrm{BH}$ at the bounce has a mass $M_\textrm{b}\sim M^2_\textrm{BH} m^{1/2}_\textrm{n}/m^{3/2}_\textrm{Pl}$, where $m_\textrm{n}$ is the mass of a neutron and $m_\textrm{Pl}$ is the reduced Planck mass. For a typical stellar black hole, $M_\textrm{b}$ is about $10^{32}$ solar masses, which is $10^6$ larger than the mass of our Universe. As the relativistic black-hole universe expands, its mass decreases until the universe becomes dominated by nonrelativistic heavy particles.