Voir la notice de l'article provenant de la source Math-Net.Ru
@article{PFMT_2019_2_a5, author = {M. A. Serdyukova and A. N. Serdyukov}, title = {A massive gravitational field in flat spacetime. {I.} {Gauge} invariance and field equations}, journal = {Problemy fiziki, matematiki i tehniki}, pages = {45--53}, publisher = {mathdoc}, number = {2}, year = {2019}, language = {en}, url = {http://geodesic.mathdoc.fr/item/PFMT_2019_2_a5/} }
TY - JOUR AU - M. A. Serdyukova AU - A. N. Serdyukov TI - A massive gravitational field in flat spacetime. I. Gauge invariance and field equations JO - Problemy fiziki, matematiki i tehniki PY - 2019 SP - 45 EP - 53 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/PFMT_2019_2_a5/ LA - en ID - PFMT_2019_2_a5 ER -
M. A. Serdyukova; A. N. Serdyukov. A massive gravitational field in flat spacetime. I. Gauge invariance and field equations. Problemy fiziki, matematiki i tehniki, no. 2 (2019), pp. 45-53. http://geodesic.mathdoc.fr/item/PFMT_2019_2_a5/
[1] A.A. Logunov, Relativistic Theory of Gravity, Nova Science Publishers, Commack, USA, 1998, 319 pp. | MR
[2] H. Bondi, T. Gold, “The field of a uniformly accelerated charge, with special reference to the problem of gravitational acceleration”, Proc. Roy. Soc., A (1955), 416–424 | MR | Zbl
[3] S. Parrott, “Radiation from a Uniformly Accelerated Charge and the Equivalence Principle”, Found. Phys., 32 (2002), 407–440 | DOI | MR
[4] E. Poisson, A. Pound, I. Vega, “The motion of point particles in curved spacetime”, Living Rev. Relativity, 14 (2011), 7–190 | DOI | Zbl
[5] D. Hilbert, Relativity, Quantum Theory and Epistemology, David Hilbert's Lectures on the Foundations of Physics, 1915–1927, eds. T. Sauer, U. Majer, Springer, Heidelberg, Germany, 2009, 795 pp. | MR | Zbl
[6] E. Noether, “Invariant Variation Problems”, Transp. Theory Statist. Phys., 1971, no. 1, 186–207 | DOI | MR | Zbl
[7] V.I. Denisov, A.A. Logunov, “The inertial mass defined in the general theory of relativity has no physical meaning”, Theoret. and Math. Phys., 51 (1982), 421–426 | DOI | MR | Zbl
[8] A.A. Logunov, M.A. Mestvirishvili, “Relativistic theory of gravitation”, Theoret. and Math. Phys., 61:3 (1985), 1170–1183 | DOI | MR
[9] A.A. Logunov, M.A. Mestvirishvili, “Relativistic theory of gravitation”, Foundations of Physics, 16 (1986), 1–26 | DOI | MR
[10] A.A. Logunov, Yu.M. Loskutov, M.A. Mestvirishvili, “Relativistic theory of gravitation and criticism of general relativity”, Theor. Math. Phys., 73 (1987), 1131–1148 | DOI | MR | Zbl
[11] S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York, 1972, 657 pp.
[12] D.S. Gorbunov, V.A. Rubakov, Introduction to the Theory of Early Universe: Hot Big Bang Theory, World Scientific, New Jersey, 2011, 473 pp. | Zbl
[13] C. Misner, K. Thorne, J.A. Wheeler, Gravitation, Freeman Co, San Francisco, 1973, 1278 pp. | MR
[14] W. Pauli, Theory of Relativity, Pergamon, London, 1958, 241 pp. | MR | Zbl
[15] A.S. Eddington, The Mathematical Theory of Relativity, Cambridge University Press, Cambridge, 1930, 270 pp. | MR
[16] A.L. Zel'manov, V.G. Agakov, Elements of the General Theory of Relativity, Nauka, M., 1989, 236 pp. (in Russian) | MR | Zbl
[17] E. Schrodinger, “Die Energiekomponeneten des Gravitationfeldes”, Phys. Zeitschr., 19 (1918), 4–7 | Zbl
[18] H. Bauer, “Uber die Energiekomponenten des Gravitationsfeldes”, Phys. Zeitschr., 19 (1918), 163–165 | Zbl
[19] P.A.M. Dirac, “The excellence of Einstein's theory of gravitation”, Einstein: the First Hundred Years, eds. M. Goldsmith, A. Mackay, J. Woudhuysen, Pergamon, 1980, 41–46 | DOI
[20] V. Fock, The Theory of Space, Time, and Gravitation, Pergamon, London, 1964, 448 pp. | MR
[21] R.P. Feynman et al., Feynman Lectures on Gravitation, Addison-Wesley, Reading, Pennsylvania, 1995, 232 pp.
[22] H. Weyl, How far can one get with a linear field theory of gravitation in flat space-time?, Amer. J. Math., 66 (1944), 591–604 | DOI | MR | Zbl
[23] A.N. Serdyukov, “A minimal relativistic model of gravitation within standard restrictions of the classical theory of fields”, Phys. of Part. and Nucl. Lett., 6 (2009), 190–201 | DOI
[24] A. Einstein, A.D. Fokker, “Nordström's Theory of Gravitation from the Point of View of the Absolute Differential Calculus”, Doc. 28, The Collected Papers of Einstein, v. 4, Princeton Univ. Press, Princeton, New Jersey, 1995, 588–597 | MR
[25] G. Nordström, “Relativitatsprinzip und Gravitation”, Phys. Z., 13 (1912), 1126–1129 | Zbl
[26] G. Nordström, “Trage und schwere Masse in der Relavitatsmechanik”, Ann. Phys. (Leipzig), 40 (1913), 856–878 | DOI | Zbl
[27] G. Nordström, “Zur Theorie der Gravitation vom Standpunkt des Relavitatsprinzip”, Ann. Phys. (Leipzig), 42 (1913), 533–554 | DOI | Zbl
[28] A. Einstein, “On the Present State of the Problem of Gravitation”, Doc. 17, The Collected Papers of Einstein, v. 4, Princeton Univ. Press, Princeton, New Jersey, 1995, 486–503 | MR
[29] L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics, v. 2, The Classical theory of fields, Butterworth-Heinemann, Oxford, 1987, 428 pp. | MR
[30] J.D. Norton, A. Einstein, “Nordström and the early demise of scalar, Lorentz covariant theories of gravitation”, Archive for History of Exact Sciences, 45 (1992), 17–94 | DOI | MR | Zbl
[31] R.H. Dicke, “Mach's principle and invariance under transformation of units”, Phys. Rev., 125 (1962), 2163–2167 | DOI | MR | Zbl
[32] M. Wellner, G. Sandri, “Scalar gravitation”, Am. J. Phys., 32 (1964), 36–39 | DOI | MR | Zbl
[33] O. Bergmann, “Scalar field theory as a theory of gravitation. I”, Am. J. Phys., 24 (1956), 38–42 | DOI | Zbl
[34] I.M. Gel'fand, R.A. Minlos, Z.Ya. Shapiro, Representations of the Rotation and Lorentz Groups and Their Applications, Pergamon, Oxford, 1963, 366 pp. | MR | Zbl
[35] E. Corinaldesi, Classical mechanics for physics graduate students, World Scientific, Syngapur, 1998, 286 pp. | MR | Zbl
[36] L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics, v. 1, Mechanics, Butterworth-Heinemann, Oxford, 1976, 170 pp. | MR
[37] M.A. Serdyukova, “The Law of Energy Momentum Conservation of Massive Spinzero Gravitational Field”, Problems of Interaction of Radiation with Matter, Proceedings of the V International Scientific Conference Dedicated to Academician B. V. Bokut (Gomel, November 14–16, 2018), v. 1, F. Skorina Gomel State University, Gomel, 2018, 193–199
[38] L. Brillouin, Relativity Reexavined, Academic Press, New York, 1970, 111 pp.
[39] S. Deser, L. Halpern, “Self-coupled scalar gravitation”, Gen. Rel. Grav., 1970, no. 1, 131–136 | DOI | MR
[40] G. 't Hooft, Introduction to General Relativity, Utrecht University, Utrecht, Netherlands, 2012, 71 pp.
[41] C. Wetterich, “Modified Gravity and Coupled Quintessence”, Modifications of Einstein's Theory of Gravity at Large Distances, Lecture Notes in Physics, 892, ed. Papantonopoulos E., Springer, 2015, 57–95 | DOI | MR
[42] I.G. Dudko, Yu.P. Vyblyi, “Scalar field with the source in the form of the stress-energy tensor trace as a darkenergy model”, Gravitation and Cosmology, 22 (2016), 368–373 | DOI | MR
[43] Yu.P. Vyblyi, A.A. Leonovich, “Interacting scalar field in the theory of gravity”, Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 2017, no. 4, 98–103 | MR