Mass of the universe in a black hole

TL;DR

This paper explores how black holes could contain new universes formed through quantum effects and torsion, resulting in a universe with a mass vastly exceeding our own, and describes the evolution of such a universe.

Contribution

It proposes a model where black hole interiors become new universes with masses proportional to the square of the black hole mass, incorporating quantum particle production and torsion effects.

Findings

Black hole interiors can form new universes with masses around 10^6 times our universe.

Quantum particle production influences the mass increase during gravitational collapse.

The universe inside a black hole evolves from ultrarelativistic to nonrelativistic matter dominance.

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.