Keywords: self-adjoint second-order equation, spinor wave function, effective potential.
@article{TMF_2018_197_3_a10,
author = {V. P. Neznamov},
title = {Second-order equations for fermions on {Schwarzschild,}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {493--509},
year = {2018},
volume = {197},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2018_197_3_a10/}
}
V. P. Neznamov. Second-order equations for fermions on Schwarzschild,. Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 3, pp. 493-509. http://geodesic.mathdoc.fr/item/TMF_2018_197_3_a10/
[1] P. A. M. Dirac, The Principles of Quantum Mechanics, Clarendon Press, Oxford, 1958 | MR
[2] Ya. B. Zeldovich, V. S. Popov, “Elektronnaya struktura sverkhtyazhelykh atomov”, UFN, 105:3 (1971), 403–440 | DOI | DOI
[3] M. V. Gorbatenko, V. P. Neznamov, “Solution of the problem of uniqueness and Hermiticity of Hamiltonians for Dirac particles in gravitational fields”, Phys. Rev. D, 82:10 (2010), 104056, 11 pp., arXiv: 1007.4631 | DOI
[4] M. V. Gorbatenko, V. P. Neznamov, “Uniqueness and self-conjugacy of Dirac Hamiltonians in arbitrary gravitational fields”, Phys. Rev. D, 83:10 (2011), 105002, 12 pp., arXiv: 1102.4067 | DOI
[5] M. V. Gorbatenko, V. P. Neznamov, “A modified method for deriving self-conjugate Dirac Hamiltonians in arbitrary gravitational fields and its application to centrally and axially symmetric gravitational fields”, J. Modern Phys., 6:3 (2015), 54289, 23 pp., arXiv: 1107.0844 | DOI
[6] J. Schwinger, “Energy and momentum density in field theory”, Phys. Rev., 130:1 (1963), 800–805 | DOI
[7] D. R. Brill, J. A. Wheeler, “Interaction of neutrinos and gravitational fields”, Rev. Modern Phys., 29:3 (1957), 465–479 | DOI | MR
[8] S. R. Dolan, Trinity hall and astrophysics group, PhD Thesis, Cavendish Laboratory, University of Cambridge, Cambridge, 2006
[9] S. Chandrasekhar, “The solution of Dirac's equation in Kerr geometry”, Proc. Roy. Soc. London Ser. A, 349:1659 (1976), 571–575 | DOI | MR
[10] S. Chandrasekhar, “Errata: The solution of Dirac's equation in Kerr geometry”, Proc. R. Soc. London Ser. A, 350:1663 (1976), 565 | DOI | MR
[11] D. N. Page, “Dirac equation around a charged, rotating black hole”, Phys. Rev. D, 14:6 (1976), 1509–1510 | DOI
[12] L. Parker, “One-electron atom as a probe of spacetime curvature”, Phys. Rev. D, 22:8 (1980), 1922–1934 | DOI
[13] V. P. Neznamov, V. E. Shemarulin, “Analysis of half-spin particle motion in Kerr–Newman field by means of effective potentials in second-order equations”, Grav. Cosmol., 24:2 (2018), 129–138 | DOI | MR
[14] M. V. Gorbatenko, V. P. Neznamov, “On the uniqueness of the Dirac theory in curved and flat spacetime”, Ann. Phys. (Berlin), 526:3–4 (2014), 195–200 | DOI
[15] F. Finster, N. Kamran, J. Smoller, S.-T. Yan, “Nonexistence of time-periodic solutions of the Dirac equation in an axisymmetric black hole geometry”, Commun. Pure Appl. Math., 53:7 (2000), 902–929 | 3.0.CO;2-4 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR
[16] I. M. Ternov, A. B. Gaina, G. A. Chizhov, “Finitnoe dvizhenie elektronov v pole mikroskopicheski malykh chernykh dyr”, Izv. vuzov. Fizika, 23:8 (1980), 56–62 | DOI
[17] D. Batic, M. Nowakowski, K. Morgan, “The problem of embedded eigenvalues for the Dirac equation in the Schwarzschild black hole metric”, Universe, 2:4 (2016), 31, 14 pp., arXiv: 1701.03889 | DOI
[18] G. Bete, E. Salpiter, Kvantovaya mekhanika s odnim i dvumya elektronami, Fizmatgiz, M., 1960 | MR
[19] V. P. Neznamov, “Impenetrable barriers for positrons in neighbourhood of superheavy nuclei with $Z>118$”, J. Phys.: Conf. Ser., 938 (2017), 012033 | DOI
[20] V. P. Neznamov, I. I. Safronov, “Statsionarnye resheniya uravneniya vtorogo poryadka dlya tochechnykh fermionov v gravitatsionnom pole Shvartsshilda”, ZhETF, 154:4(10) (2018), 761–773 | DOI
[21] V. P. Neznamov, I. I. Safronov, V. E. Shemarulin, “Statsionarnye resheniya uravneniya vtorogo poryadka dlya fermionov v prostranstve-vremeni Raissnera–Nordstrema”, ZhETF, 154:4(10) (2018), 802–825 | DOI
[22] V. P. Neznamov, I. I. Safronov, V. E. Shemarulin, “Statsionarnye resheniya uravneniya vtorogo poryadka dlya fermionov v prostranstve-vremeni Kerra–\allowbreakNyumena”, ZhETF, 2019 (to appear)
[23] C. L. Pekeris, K. Frankowski, “Solution of Dirac's equation in Reissner–Nordstroem geometry”, Proc. Natl. Acad. Sci. USA, 83:7, 1978–1982 | DOI | MR
[24] G. T. Horowitz, D. Marolf, “Quantum probes of spacetime singularities”, Phys. Rev. D, 52:10 (1995), 5670–5675 | DOI | MR