Volume 7, Issue 4, August 2019, Page: 45-49
The Dynamics of the Neutron Complexes: From Neutron Star to Black Hole
Yuriy Nikolaevich Zayko, Russian Presidential Academy of National Economy and Public Administration, Stolypin Volga Region Institute, Saratov, Russia
Received: Jun. 27, 2019;       Accepted: Sep. 28, 2019;       Published: Oct. 11, 2019
DOI: 10.11648/j.ijass.20190704.11      View  133      Downloads  21
Abstract
The mechanism of the appearance of neutron complexes, which at the final stage of their development, evolve into neutron stars, is described. It is shown that for a quantitative description it is necessary to use a generalization of the Newton-Schrödinger equations taking into account the next terms in the decomposition of explicit Dirac – Maxwell equations on c-2. In this approximation, the problem is described by the well-known Gross-Pitaevskii equation, the numerical analysis of which is performed for the spherically symmetric case. The result depends on the value of the parameter α equal to the ratio of the gravitational radius of the neutron complex to twice the Compton wavelength. For small values of α <0.5, the solutions describe a neutron star; for α > 0.5, the description corresponds to its gravitational collapse. This is consistent with the analysis of the general 3-dimensional case.
Keywords
Schrödinger-Newton Equations, Gravitational Potential, Neutron Star, Bosonic Condensate, Gross-Pitaevskii Equation
To cite this article
Yuriy Nikolaevich Zayko, The Dynamics of the Neutron Complexes: From Neutron Star to Black Hole, International Journal of Astrophysics and Space Science. Vol. 7, No. 4, 2019, pp. 45-49. doi: 10.11648/j.ijass.20190704.11
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Yu. N. Zayko, Calculation of the Effective Gravitational Charge using the Newton-Schrödinger Equations, International Journal of Scientific and Innovative Mathematical Research (IJSIMR) V. 7, № 6, 2019, PP 17-22.
[2]
R. Harrison, I. Moroz and K. P. Tod, A numerical study of the Schrődinger –Newton equations, Nonlinearity 16, (2003), pp. 101–122.
[3]
L. D. Landau, E. M. Lifshitz (1977). Quantum Mechanics: Non-Relativistic Theory. Vol. 3 (3rd ed.), Pergamon Press.
[4]
V. B. Berestetskii, E. M. Lifshitz, L. P. Pitaevskii (1971). Relativistic Quantum Theory. Vol. 4 (1st ed.), Pergamon Press.
[5]
A. D. Polyanin, V. F. Zaitsev. Handbook of Nonlinear Partial Differential Equations, (Handbooks of Mathematical Equations), 2nd Edition, Chapman and Hall/CRC, 2011.
[6]
R. Penrose, On gravity’s role in quantum state reduction, Gen. Rel. Grav. 28 (1996) pp. 581-600.
[7]
R. Penrose, Quantum computation, entanglement and state reduction, Phil. Trans. R. Soc. (London) A 356 (1998) 1927.
[8]
I. M. Moroz, R. Penrose, and P. Tod, Spherically-symmetric solutions of the Schrődinger–Newton equations, Class. Quantum Grav. 15 (1998) 2733–2742.
[9]
L. D. Landau, E. M. Lifshitz (1980). Statistical Physics. Vol. 5 (3rd ed.). Butterworth-Heinemann.
[10]
E. M. Lifshitz, L. P. Pitaevskii (1980). Statistical Physics, Part 2: Theory of the Condensed State. Vol. 9 (1st ed.). Butterworth-Heinemann.
[11]
R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, H. C. Morris, Solitons and Nonlinear Wave Equations (1982), Academic Press Inc., (London).
[12]
W. A. Strauss (1978) Nonlinear Invariant Wave Equations, In Velo G and Wightman A (Ed.), Invariant Wave Equations, Berlin, Springer-Verlag.
[13]
P. S. Lomdahl, O. H. Olsen and P. L. Christiansen (1980) Return and Collapse of Solutions to the Nonlinear Schrӧdinger Equation in Cylindrical Symmetry, Phys. Lett., 78A, 125-128.
[14]
K. Konno and H. Suzuki (1979) Self-focusing of Laser Beam in Nonlinear Media, Physica Scripta, 20, 382-386.
[15]
V. E. Zakharov and V. S. Synakh (1975) The Nature of the Self-focusing Singularity, Zh. Eksp. Teor. Fiz. 68, 940-94.
[16]
M. Rozner and V. Desjacques (2018) Backreaction of Axion Coherent Oscillations, arXiv: 1804.10417v1 [astro-ph.CO] 27 Apr 2018.
[17]
J. Eby, M. Leembruggen, L. Street, P. Suranyi, and L. C. R. Wijewardhana (2019) Global View of QCD Axion Stars, arXiv: 1905.00981v3 [hep-ph] 9 Sep 2019.
[18]
J. R. Lonnborn, A. Melatos, and B. Haskell (2019) Collective, Glitch-like Vortex Motion in a Neutron Star with an Annular Pinning Barrier, arXiv: 1905.02877v1 [astro-ph.HE] 8 May 2019.
[19]
T. Harko (2019) Jeans Instability and Turbulent Gravitational Collapse of Bose-Einstein Condensate Dark Matter Halos arXiv: 1909.05022v1 [gr-qc] 9 Sep 2019.
[20]
S. Sarkar, C. Vaz and L. C. R. Wijewardhana (2018) Gravitationally Bound Bose Condensates with Rotation, arXiv: 1711.01219v2 [astro-ph. GA] 15 May 2018.
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