Quantum vacuum effects on the final fate of a collapsing ball of dust. (English) Zbl 1377.83058
Summary: We consider the quantum vacuum effects of the massless scalar fields that are non-minimally coupled to the background geometry of a collapsing homogeneous ball of dust. It is shown that for a definite range of coupling constants, there are repulsive quantum vacuum effects, capable of stopping the collapse process inside the black hole and precluding the formation of singularity. The final fate of the collapse will be a black hole with no singularity, inside which the matter stays balanced. The density of the final static matter will be close to the Planck density. We show that the largest possible radius of the stable static ball inside a black hole with Schwarzschild mass \(M\) is given by \( {\left(\frac{1}{90\pi} \frac{M}{m_p}\right)}^{{1}/{3}}{\ell}_p \). If the black hole undergoes Hawking radiation, the final state will be an extremal quantum-corrected black hole, with zero temperature, with a remnant of matter inside. We show that the resolution of singularity is not disrupted under Hawking radiation.
MSC:
| 83C75 | Space-time singularities, cosmic censorship, etc. |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
| 83C55 | Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) |
| 83C57 | Black holes |
| 80A10 | Classical and relativistic thermodynamics |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
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