Abstract
Using the braid group topological approach to quantum statistics we demonstrate that for strong gravitational field occurring in neutron star merger with mass exceeding the Tolman, Oppenheimer and Volkoff limit the quantum statistics of particles beneath the photon sphere decays, which results in an instant relief of quantum degeneracy pressure in the star. This causes a rapid shrink of the matter to a black hole with quite different quantum collective character of particles. The scheme of neutron Fermi sphere collapse is proposed as the possible isotropic source of short giant gamma-ray bursts. The similar quantum mechanism of collapse of Fermi spheres of electrons and protons in plasma of accretion disc in vicinity of the Schwarzschild horizon of galactic black hole is able to elucidate the giant luminosity of remote quasars. The efficiency of the mass to energy conversion via collapse of the Fermi sphere is ca. 30 %, not reachable for any other known physical process except of the matter-antimatter annihilation.
Highlights
Using the braid group topological approach to quantum statistics we demonstrate that for strong gravitational field occurring in neutron star merger with mass exceeding the Tolman, Oppenheimer and Volkoff limit the quantum statistics of particles beneath the photon sphere decays, which results in an instant relief of quantum degeneracy pressure in the star
In accretion disc of quasars, the gravitation energy accumulated in Fermi spheres of electrons and protons in ultra-dense plasma approaching the Schwarzschild surface of the super-massive central black hole is released for the same reason as in a neutron star, when the dense Fermi liquid passes inward the innermost unstable orbit near the event horizon
By analysis of particle trajectories beneath the Schwarzschild surface and beneath the photon sphere we have concluded that the quantum statistics cannot be assigned to particles in these regions, because of specific homotopy of admissible particle trajectories here, which locally precludes the braid group definition
Summary
Quantum statistics is the consequence of indistinguishability of identical particles and is a collective topological effect (cf. ref. [11], where the topological roots of quantum statistics have been highlighted for the first time). In the case of particles between the event horizon and the photon sphere (the sphere with the radius of the innermost unstable circular orbit of a black hole, cf appendix B), the homotopy class of trajectories of particles radically changes, which locally dismisses the conventional quantum statistics because trajectories for particle exchanges do not exist there This can be described in terms of Schwarzschild coordinates and holds in any other metrics describing the same gravitational singularity but expressed in different coordinate systems like. In the present paper we propose to apply the homotopy topological approach to quantum statistics in 4D spacetime (3D spatial manifold in gravitationally curved spacetime) for the new concept of the rapid local decay of quantum statistics (and, in particular, local washing out of Pauli exclusion principle for particles bereft of their fermionic character) in the region of Schwarzschild zone below the innermost unstable circular orbit, when a neutron star merger gains the mass above the TOV-limit
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