The field-theoretic approach in general relativity and other metric theories. A review

The field-theoretic approach in general relativity and other metric theories. A review

Автор: Petrov A. N., Pitts J. B.

Журнал: Пространство, время и фундаментальные взаимодействия @stfi

Рубрика: Гравитация, космология и фундаментальные поля

Статья в выпуске: 4 (29), 2019 года.

Бесплатный доступ

The representation of General Relativity (GR) and other metric theories of gravity in field-theoretic form on a background is reviewed. The gravitational field potential (metric perturbation) and other physical fields are propagated in an auxiliary background spacetime, which may be curved and may lack symmetries. Such a reformulation of a metric theory is exact and generally equivalent to its initial formulation in the standard geometrical form. The formalism is Lagrangian-based, in that the equations for the propagating fields are obtained by varying the related Lagrangian, as are the background field equations. A new sketch of how to include spinor fields is included. Conserved quantities are obtained by applying the Noether theorem to the Lagrangian as well. Conserved currents are expressed through divergences of antisymmetric tensor densities (superpotentials), connecting local perturbations with quasi-local conserved quantities. The gauge dependence due to the background metric is studied, reflecting the so-called non-localizability of gravitational energy in exact mathematical expressions formally, an infinity of localized energy distributions that, combined with the material energy, satisfy the continuity equation...

Еще

Conservation laws, general relativity, modified metric theories

Короткий адрес: https://sciup.org/142224159

IDR: 142224159   |   DOI: 10.17238/issn2226-8812.2019.4.66-124

Список литературы The field-theoretic approach in general relativity and other metric theories. A review

  • Petrov A.N. Nonlinear Perturbations and Conservation Laws on Curved Backgrounds in GR and Other Metric Theories. Chapter in: Classical and Quantum Gravity Research. Eds: Christiansen M.N., Rasmussen T.K. New York: Nova Science Publishers; 2008, pp. 79-160.
  • Petrov A.N. The dynamical space-time as a field configuration in a background space-time. Chapter In: Ether space-time and cosmology. Volume 1: Modern ether concepts, relativity and cosmology. Eds: Duffy M.C., Levy J., Krasnoholovets V. Liverpool: PD Publications; 2008, pp. 257-303.
  • Petrov A.N., Kopeikin S.M., Lompay R.R., Tekin B. Metric Theories of Gravity: Perturbations and Conservation Laws. Berlin: de Gruyter; 2017.
  • Petrov A.N. Gen. Relat. Grav., 2018, 50(1), pp. 6-30. ArXiv:1712.09445 [gr-qc].
  • Petrov A.N. Class. Quantum Grav., 2009, 26(13), 135010(16pp). Corrigendum: Class. Quantum Grav., 2010, 27(6), 069801(2pp). arXiv:0905.3622 [gr-qc].
  • Petrov A.N. Class. Quantum Grav., 2019, 36(23), 235021(22pp). ArXiv:1903.05500 [gr-qc].
  • Kostro L. Einstein and the ether. Montreal: Apeiron; 2000.
  • Norton J.D. Archive for History of Exact Sciences, 1992, 45(1), pp. 17-94.
  • Giulini D. Studies in History and Philosophy of Modern Physics, 2008, 39(1), pp. 154-180. ArXiv:gr-qc/0611100.
  • Einstein A., Fokker A.D. Die Nordströmsche Gravitationstheorie vom Standpunkt des absoluten Differentialkalküls, Annalen der Physik, 1914, 44, pp. 321-328. English translation in The Collected Papers of Albert Einstein. Ed: Anna B., Howard D., Volume 4. Princeton: The Hebrew University of Jerusalem and Princeton University Press; 1996, pp. 293-299.
  • Kraichnan R.H. Phys. Rev., 1955, 98(4), pp. 1118-1122.
  • Freund P.G.O., Nambu Y. Phys. Rev., 1968, 174(5), pp. 1741-1743.
  • Deser S., Halpern L. Gen. Relat. Grav., 1970, 1(2), pp. 131-136.
  • Pitts J.B. Gen. Relat. Grav., 2011, 43(3), pp. 871-895. ArXiv:1010.0227 [gr-qc].
  • Stachel J. The Story of Newstein, Or, Is Gravity Just Another Pretty Force? Chapter in: The Genesis of General Relativity, Volume 4. Gravitation in the Twilight of Classical Physics: The Promise of Mathematics. Eds: Renn J., Schemmel M. Dordrecht: Springer; 2007, pp. 1041-1078.
  • Freund P.G.O., Maheshwari A., Schonberg E. Astrophys. J., 1969, 157(August), pp. 857-867.
  • Schucking E.L. The introduction of the cosmological constant. Chapter in: Gravitation and Modern Cosmology: The Cosmological Constant Problem, Volume in honor of Peter Gabriel Bergmann's 75th birthday. Eds: Zichichi A., de Sabbata V., Sánchez N. New York: Plenum; 1991, pp. 185-187.
  • Pitts J.B. Cosmological constant Λ vs. massive gravitons: A case study in General Relativity exceptionalism vs. particle physics egalitarianism. Chapter in: The Renaissance of General Relativity. Einstein Studies. Eds: Blum A., Lalli R., Renn J. Birkhäuser, 2020. ArXiV:1906.02115.
  • Pitts J.B. The British Journal for the Philosophy of Science, 2011, 62(2), pp. 259-299.
  • Watt K., Misner C.W. Relativistic scalar gravity: A laboratory for numerical relativity. 1999. ArXiv:gr-qc/9910032.
  • Brown H.R. Physical Relativity: Space-time Structure from a Dynamical Perspective. New York: Oxford University Press; 2005.
  • Pitts J.B. Studies in History and Philosophy of Modern Physics, 2016, 53(February), pp. 73-92. ArXiv:1509.03303 [physics.hist-ph].
  • Pitts J.B. Studies in History and Philosophy of Modern Physics, 2019, 67(August), pp. 191-198; Invited reviewed contribution to special issue on Harvey Brown's Physical Relativity 10 years later. Ed: Saunders S. ArXiv:1710.06404 [physics.hist-ph].
  • Pitts J.B. Erkenntnis, 2018, 83(March), pp. 135-161. ArXiv:1803.11192 [physics.hist-ph].
  • Nachtmann O., Schmidle H., Sexl R.U. Commun. Math. Phys., 1969, 13(3), pp. 254-256.
  • Van Nieuwenhuizen P. Nucl. Phys. B, 1973, 60(1), pp. 478-492.
  • Deser S. Gen. Relat. Grav., 1970, 1(1), pp. 9-18. ArXiv:gr-qc/0411023.
  • Davies P.C.W., and Fang J. Proc. R. Soc. London A, 1982, 381(1781), pp. 469-478.
  • Pitts J.B., Schieve W.C. Gen. Relat. Grav., 2001, 33(8), pp. 1319-1350. ArXiv:gr-qc/0101058.
  • Boulware D.G., Deser S. Phys. Rev. D, 1972, 6(12), pp. 3368-3382.
  • De Rham C., Gabadadze G., Tolley A.J. Phys. Rev. Lett., 2011, 106(23), 231101(4pp). ArXiv:1011.1232 [hep-th].
  • Hassan S.F., Rosen R.A. J. High En. Phys., 2012, 2012(123), pp. 0-16. ArXiv:1111.2070 [hep-th].
  • Maheshwari A. Nuovo Cim. A, 1972, 8(2), pp. 319-330.
  • Pitts J.B. Ann. Phys., 2016, 365(February), pp. 73-90. ArXiv:1505.03492 [gr-qc].
  • Van Dam H., Veltman M. Nucl. Phys. B, 1970, 22(2), pp. 397-411.
  • Van Dam H., Veltman M. Gen. Relat. Grav., 1972, 3(3), pp. 215-220.
  • Iwasaki Y. Phys. Rev. D, 1970, 2(10), pp. 2255-2256.
  • Vainshtein A.I. Phys. Lett. B, 1972, 39(3), pp. 393-394.
  • Deffayet C., Dvali G., Gabadadze G., Vainshtein A.I. Phys. Rev. D, 2002, 65(4), 044026(10pp). ArXiv:hepth/0106001.
  • Pitts J.B. Studies in History and Philosophy of Modern Physics, 2016, 54(May), pp. 52-72. ArXiv:1604.03038 [physics.hist-ph].
  • Pitts J.B. Studies in History and Philosophy of Modern Physics, 2016, 56(November), pp. 60-69. ArXiv:1611.02673 [physics.hist-ph].
  • Norton J. How Einstein found his field equations, 1912-1915. Chapter in: Einstein and the History of General Relativity; Proceedings of the 1986 Osgood Hill Conference, volume 1 of Einstein Studies. Eds: Howard D., Stachel J. Boston: Birkhäuser; 1989, pp. 101-159.
  • Renn J., Sauer T. Heuristics and mathematical representation in Einstein's search for a gravitational field equation. Chapter in: The Expanding Worlds of General Relativity, volume 7 of Einstein Studies. Eds: Goenner H., Renn J., Ritter J., Sauer T. Boston: Birkhäuser; 1999, pp. 87-125.
  • Janssen M. Annalen der Physik, 2005, 14(S1), pp. 58-85.
  • Brading K. A note on general relativity, energy conservation, and Noether's theorems. Chapter in: he Universe of General Relativity, volume 11 of Einstein Studies. Eds: Kox A.J., Eisenstaedt J. Boston: Birkhäuser; 2005, pp. 125-135.
  • Renn J. Standing on the Shoulders of a Dwarf: A Triumph of Einstein and Grossmann's Erroneous Entwurf Theory. Chapter in: he Universe of General Relativity, volume 11 of Einstein Studies. Eds: Kox A.J., Eisenstaedt J. Boston: Birkhäuser; 2005, pp. 39-51.
  • Renn J. Before the Riemann tensor: The emergence of Einstein's double strategy. Chapter in: he Universe of General Relativity, volume 11 of Einstein Studies. Eds: Kox A.J., Eisenstaedt J. Boston: Birkhäuser; 2005, pp. 53-65.
  • Janssen M., Renn J. Untying the knot: How Einstein found his way back to field equations discarded in the Zurich notebook. Chapter in: The Genesis of General Relativity, Volume 2: Einstein's Zurich Notebook: Commentary and Essays. Ed: Renn J. Dordrecht: Springer; 2007, pp. 839-925.
  • Renn J., Sauer T. Pathways out of classical physics: Einstein's double strategy in his seach for the gravitational field equations. Chapter in: The Genesis of General Relativity, Volume 1: Einstein's Zurich Notebook: Introduction and Source. Ed: Renn J. Dordrecht: Springer; 2007, pp. 113-312.
  • Van Dongen J. Einstein's Unification. Cambridge: Cambridge University Press; 2010.
  • Noether E. Invariante Variationsprobleme. Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 1918, pp. 235-257. Translated as Invariant Variation Problems by M. A. Tavel; Transport Theory and Statistical Physics, 1971, 1, pp. 183-207. ArXiv:physics/0503066 [physics.histph].
  • DeWitt B.S. Dynamical theory of groups and fields. New York: Gordon and Breach; 1965. 54.
  • Isaacson R.A. Phys. Rev., 1968, 166(5), pp. 1272-1280.
  • Efroimsky M. Class. Quantum Grav., 1992, 9(12), pp. 2601-2614.
  • Efroimsky M. Phys. Rev. D, 1994, 49(12), pp. 6512-6520.
  • Svitek O., Podolsky J. Class. Quantum Grav., 2014. 21(14), pp. 3579-3585. ArXiv:gr-qc/0406093.
  • Galtier S., Nazarenko S.V., Buchlin E., Thalabard S. Physica D: Nonlinear Phenomena, 2019, 390(March), pp. 84-88. ArXiv:1809.07623 [gr-qc].
  • Barta D., Vasuth M. Int. J. Mod. Phys. D, 2018, 27(4), 1850040(11pp). ArXiv:1708.05576 [gr-qc].
  • Misner C.W., Thorne K.S, Wheller J.A. Gravitation. San Francisco: Freeman; 1973.
  • Pitts J.B. Gen. Relat. Grav., 2010, 42(3), pp. 601-622. ArXiv:0902.1288 [gr-qc].
  • Kosmann-Schwarzbach Y. The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century. New York: Springer; 2011.
  • Papapetrou A. Proc. R. Irish Ac., 1948, 52(2), pp. 11-23.
  • Chang C.-C., Nester J.M., Chen C.-M. Phys. Rev. Lett., 1999, 83(10), pp. 1897-1901. ArXiv:gr-qc/9809040.
  • Chang C.-C., Nester J.M., Chen C.-M. Energy-momentum (Quasi-)Localization for gravitating systems. In: The Proceedings of the 4-th Int. Workshop on Gravitation and Astrophysics: Beijing Normal University, China, October 10-15, 1999. Eds: Liu L., Luo J., Li X-Z., Hsu J.-P. Singapore: World Scientific; 2000, pp. 163-173. ArXiv:gr-qc/9912058.
  • Bauer H. Physikalische Zeitschrift, 1918, 19(8), pp. 163-165.
  • Weisberg J.M., Nice D.J., and Taylor J.H. Astrophys. J., 2010, 722(2), pp. 1030-1034. ArXiv:1011.0718 [asrto-ph.GA].
  • Abbott B.P., and etc. (LIGO-Virgo Scientific Collaborations) Phys. Rev. Lett., 2016, 116(22), 221101(17pp). ArXiv:1602.03841 [gr-qc]. Erratum Phys. Rev. Lett., 2018, 121(12), p. 129902.
  • Abbott B.P., and etc. (LIGO-Virgo Scientific Collaborations) Phys. Rev. Lett., 2016, 116(24), 241103(14pp). ArXiv:1606.04855 [gr-qc].
  • Abbott B.P., and etc. (LIGO-Virgo Scientific Collaborations) Phys. Rev. X, 2016, 116(4) 041015(39pp). ArXiv:1606.04856 [gr-qc].
  • Szabados L.B. Quasi-Local Energy-Momentum and Angular Momentum in General Relativity. Living Reviews in Relativity, 12(4), 2009; http://www.livingreviews.org/lrr-2009-4
  • Nandi K.K., Islam A. Am. J. Phys., 1995, 63(3), pp. 251-256.
  • Sotiriou T.P. Faraoni V. Rev. Mod. Phys., 2010, 82(1), pp. 451-497. ArXiv:0805.1726 [gr-qc]. 75.
  • Lovelock D. J. Math. Phys., 1971, 12(3), pp. 498-501.
  • Kopeikin S.M., Petrov A.N. Phys. Rev. D, 2013, 87(4), 044029(46pp). ArXiv:1301.5706 [gr-qc].
  • Kopeikin S.M., Petrov A.N. Ann. Phys., 2014, 350(November), pp. 379-440. ArXiv:1407.3846 [gr-qc].
  • Petrov A.N., Kopeikin S.M. Post-Newtonian approximations in cosmology. Chapter in: Frontiers in Relativistic Celestial Mechanics. Volume 1: Theory. Series: De Gruyter studies in mathematical physics. v. 21. Ed: Kopeikin S.M. Berlin: De Gruyter, 2014; pp. 295-392.
  • Kopeikin S.M., Petrov A.N. Equations of Motion in an Expanding Universe. Chapter in: Equations of Motion in Relativistic Gravity, Series: Fundamental Theories of Physics, v. 179. Eds: Puetzfeld D., Lämmerzahl C., Schutz B. Berlin: Springer, 2015; pp. 689-757.
  • Petrov A.N. Int. J. Mod. Phys. D, 1995, 4(4), pp. 451-478.
  • Petrov A.N. Int. J. Mod. Phys. D, 1997, 6(2), pp. 239-261.
  • Baskaran D., Lau S.R., Petrov A.N. Ann. Phys., 2003, 307(1), pp. 90-131. ArXiv:gr-qc/0301069.
  • Schouten J.A. Ricci-Calculus: An Introduction to Tensor Analysis and Its Geometrical Applications. Berlin: Springer (2nd edition); 1954.
  • Anderson J.L. Principles of Relativity Physics. New York: Academic; 1967.
  • Israel W. Differential Forms in General Relativity. Dublin: Dublin Institute for Advanced Studies (2-nd edition); 1979.
  • Weinberg S. Gravitation and Cosmology. New York: Wiley; 1972.
  • Thirring W. Ann. Phys., 1961, 16(1), pp. 96-117.
  • Grishchuk L.P., Petrov A.N., Popova A.D. Commun. Math. Phys., 1984, 94(3), pp. 379-396.
  • Grishchuk L.P. Chapter in: Current Topics in Astrofundamental Physics, Eds: Sanchez N., Zichichi A. Singapore: World Scientific; 1992, pp. 435-462.
  • Popova A.D, Petrov A.N. Int. J. Mod. Phys. A, 1988, 3(11), pp. 2651-2679.
  • Boulware D. C., Deser S. Ann. Phys., 1975, 89(1), pp. 193-240.
  • Pitts J.B., Schieve W.C. Theor. Math. Phys, 2007, 151(May), pp. 700-717. ArXiv:gr-qc/0503051. 94. Pitts J.B. Gen. Relat. Grav., 2012, 44(February), pp. 401-426. ArXiv:1110.2077.
  • Ogievetsky V.I., Polubarinov I.V. Ann. Phys., 1965, 35(2), pp. 167-208.
  • Levi-Civita T. The Absolute Differential Calculus: Calculus of Tensors. London: Blackie and Son; 1926. 97. Rosen N. Phys. Rev., 1940, 57(2), pp. 147-150.
  • Rosen N. Phys. Rev., 1940, 57(2), pp. 150-153.
  • Popova A.D., Petrov A.N. Int. J. Mod. Phys. A, 1993, 8(16), pp. 2683-2707.
  • Popova A.D., Petrov A.N. Int. J. Mod. Phys. A, 1993, 8(16), pp. 2709-2734.
  • Petrov A.N., Popova A.D. Int. J. Mod. Phys. D, 1994, 3(2), pp. 461-483.
  • Petrov A.N., Popova A.D. Gen. Relat. Grav., 1994, 26(11), pp. 1153-1164.
  • Petrov A.N. Mod. Phys. Lett. A, 1991, 6(23), pp. 2107-2111.
  • Ogievetski˘i V.I., Polubarinov I.V. Soviet Physics JETP, 1965, 21(6), pp. 1093-1100.
  • Pitts J.B. Studies in History and Philosophy of Modern Physics, 2012, 43(1), pp. 1-24. ArXiv:1111.4586.
  • Shirafuji T. Prog. Theor. Phys., 1979, 62(3), pp. 802-822.
  • Petrov A.N. Class. Quantum Grav., 1993, 10(12), pp. 2663-2673.
  • Howard D. Point coincidences and pointer coincidences: Einstein on the invariant content of space-time theories. Chapter in: The Expanding Worlds of General Relativity, volume 7 of Einstein Studies. Eds: Goenner H., Renn J., Ritter J., Sauer T. Boston: Birkhäuser; 1999, pp. 463-500.
  • Pinto-Neto N., Trajtenberg P.I. Brazilian Journal of Physics, 2000, 30(1), pp. 181-188. 110. Brans C., Dicke R.H. Phys. Rev., 1961, 124(3), pp. 925-935.
  • Kopeikin S., Vlasov I. Phys. Rep. 2004, 400(4-6), pp. 209-318. ArXiv:gr-qc/0403068.
  • Horndeski G.W. Int. J. Theor. Phys., 1974, 10(6), pp. 363-384.
  • Tyutin I.V., Fradkin E.S Soviet Journal of Nuclear Physics, 1972, 15(3), pp. 331-334.
  • Vainshtein A. Surveys in High Energy Physics, 2006, 20(1-4), pp. 5-18.
  • Hinterbichler K. Rev. Mod. Phys., 2012, 84(2), pp. 671-7102. ArXiv:1105.3735 [hep-th].
  • De Rham C. Living Rev. Relat., 17(7), 2014. ArXiv:1401.4173 [hep-th]; 10.12942/lrr-2014-7 117. Gupta S.N. Phys. Rev., 1954, 96(6), pp, 1683-1685.
  • DOI: 10.12942/lrr-2014-7117.GuptaS.N.Phys.Rev
  • Thorne K.S., Lee D.L., Lightman A.P. Phys. Rev D, 1973, 7(12), pp. 3563-3578.
  • Pitts J.B. Studies in History and Philosophy of Modern Physics, 2006, 37(2), pp. 347-371. ArXiv:gr-qc/0506102.
  • Gupta S.N. Proc. Phys. Soc. A, 1952, 65(8), pp. 608-619.
  • Huggins E.R. Quantum Mechanics of the Interaction of Gravity with Electrons: Theory of a Spin-Two Field Coupled to Energy. Pasadena: PhD thesis, California Institute of Technology 1962; https://thesis.library.caltech.edu/6592
  • Feynman R.P. Acta Physica Polonica, 1963, 24(6), pp. 697-722.
  • Veltman M. Quantum theory of gravitation. Chapter in: Les Houches Session XXVIII, 28 Juillet-6 Septembre 1975: Méthodes en Théorie des Champs/Methods in Field Theory. Eds: Balian R., Zinn-Justin J. Amsterdam: North-Holland (2-nd edition); 1981, pp. 265-327.
  • Lotze H. Metaphysik. Drei Bücher der Ontologie, Kosmologie, und Psychologie. Leipzig: S.Hirzel; 1879. Website: gallica.bnf.fr (Bibliothèque nationale de France).
  • Poincaré H. Science and Hypothesis. In: The Foundations of Science. Pennsylvania: The Science Press, Lancaster; 1913. Translated by George Bruce Halsted, reprinted 1946; French original 1902.
  • Reichenbach H. The Philosophy of Space and Time. New York: Dover; 1958.
  • Landau L.D., Lifshitz E.M. The classical theory of fields. London: Addison-Wesley and Pergamon; 1971. 128. Abbott L.F., Deser S. Nuclear Phys. B, 1982, 195(1), pp. 76-96. (1982).
  • Deser S. Class. Quantum Grav., 1987, 4(4), pp. L99-L105.
  • Katz J., Bičák J., Lynden-Bell D. Phys. Rev. D, 1997, 55(10), pp. 5957-5969. ArXiv:gr-qc/0504041. 131. Petrov A.N., Katz J. Proc. R. Soc. London A, 2002, 458(2018), pp. 319-337. ArXiv:gr-qc/9911025.
  • Petrov A.Z. Einstein spaces. London: Pergamon Press; 1969. 133. Traschen J. Phys. Rev. D, 1985, 31(2), pp. 283-289.
  • Traschen J., Eardley D.M. Phys. Rev. D, 1986, 34(6), pp. 1665-1679.
  • Uzan J.-P., Deruelle N., Turok N. Phys. Rev. D, 1998, 57(12), pp. 7192-7199.
  • Petrov A.N., Narlikar J.V. Found. Phys., 1996, 26(9), pp. 1201-29. Erratum: Found. Phys, 1998, 28(6), pp. 1023-1025.
  • Petrov A.N. Found. Phys. Lett., 2005, 18(5), 477-489. ArXiv:gr-qc/0503082.
  • Petrov A.N. Astron. Astrophys. Trans., 1992, 1(3), pp. 195-205.
  • Narlikar J.V. Chapter in: A Random Walk in Relativity and Cosmology. Eds: Dadhich N., Krishna Rao J., Narlikar J.V., Vishevara C.V. New Delhi: Wiley Eastern Limited; 1985, pp. 171-183.
  • Pitts J.B., Schieve W.C. Found. Phys., 2004, 34(2), pp. 211-238. ArXiv:gr-qc/0406102.
  • Pitts J.B., Schieve W.C. Found. Phys., 2004, 33(2), pp. 1315-1321. ArXiv:gr-qc/0406103.
  • Pitts J. B., Schieve W. C. Excerpt from first author's dissertation, supervised by second author, The University of Texas at Austin, 2001. arXiv:gr-qc/0111004.
  • Fock V.A. Theory of space, time and gravitation. London: Pergamon; 1959. 144. Finkelstein D. Phys. Phys., 1958, 110(4), pp. 965-967.
  • Oppenheimer J.R., Snyder H. Phys. Rev., 1939, 56(5), pp. 455-459.
  • Kanai Y., Siino M., Hosoya A. Prog. Theor. Phys., 2011, 125(May), pp. 1053-1065. ArXiv:1008.0470 [gr-qc].
  • Painlevé P. C. R. Acad. Sci. (Paris), 1921, 173(Octobre), pp. 677-680.
  • Gullstrand A. Arkiv. Mat. Astron. Fys., 1922, 16(8), pp. 1-15.
  • Hamilton A.J.S., Lisle J.P. Am. J. Phys., 2008, 76(6), pp. 519-532. ArXiv:gr-qc/0411060.
  • Bondi H., Metzner A.W.K., Van der Berg M.J.C. Proc. R. Soc. A London, 1962, 269(1336), pp. 21-52.
  • Rund H. Abhandl. Math. Sem. Univ. Hamburg, 1966, 29(3-4), pp. 243-262.
  • Lovelock D. J. Math. Phys., 1971, 12(3), pp. 498-501.
  • Arenas-Henriquez G., Miskovic O., Olea O. J. High En. Phys., 2017, 2017(11), 128(21pp). ArXiv:1710.08512 [hep-th].
  • Senturk C., Sisman T.C., Tekin B. Phys. Rev. D, 2012, 86(12), 1240307(7pp). ArXiv:1209.2056 [hep-th].
  • Adami H., Setare M.R., Sisman T.C., Tekin B. Phys. Rep., 2019, 834-835(November), pp. 1-85. ArXiv:1710.07252 [hep-th].
  • Kofinas G., Olea R. J. High En. Phys., 2007, 2007(11), 069(20pp). ArXiv:0708.0782 [hep-th].
  • Dadhich N., Ghosh S.G., Jhingan S. Phys. Lett. B, 2012, 711(2), pp. 196-198. ArXiv:1202.4575 [gr-qc].
  • Dadhich N., Ghosh S.G., Jhingan S. Phys Rev. D, 2013, 88(8), 084024(9pp). ArXiv:1308.4312 [gr-qc].
  • Dadhich N. Euro. Phys. J. C, 2016, 76(February), 104(7pp). ArXiv:1506.08764 [gr-qc]. 160. Fierz M., Pauli W. Proc. R. Soc. A, 1939, 173(953), pp. 211-232.
  • Pauli W., Fierz M. Helvetica Physica Acta, 1939, 12(4), pp. 297-300.
  • Fierz M. Helvetica Physica Acta, 1939, 12(1), pp. 3-37.
  • DeWitt B.S. I. The Theory of Gravitational Interactions. II. The Interaction of Gravitation with Light. PhD thesis 1949. Harvard: Harvard University; 1949.
  • DeWitt B.S., DeWitt C.M. Phys. Rev., 1952, 87(1), pp. 116-122.
  • Van Nieuwenhuizen P. Phys. Rev. D, 1981, 24(12), pp. 3315-3318.
  • Woodard R.P. Phys. Lett. B, 1984, 148(6), pp. 440-444.
  • Bilyalov R.F. Russian Mathematics (Iz. VUZ), 2002, 46(11), pp. 6-23.
  • Deffayet C., MouradJ., Zahariade G. J. High En. Phys., 2013, 2013(86). ArXiv:1208.4493 [gr-qc].
  • Bilyalov R. F. Theor. Math. Phys., 1992, 90(3), pp. 252-259.
  • Higham N.J. Numerical Algorithms, 1997, 15(2), pp. 227-242.
  • Higham N.J. Linear Algebra and Its Applications, 1987, 88-89(April), pp. 405-430.
  • Bourguignon J.-P., Gauduchon P. Commun. Math. Phys., 1992, 144(3), pp. 581-599.
  • Kuchař K. Canonical quantization of gravity. Chapter in: Relativity, Astrophysics, and Cosmology. Ed: Israel W. Dordrecht: D.Reidel; 1973, pp. 237-288.
  • Delbourgo R., Salam A. Lett. Nuovo Cim., 1975, 12(9), pp. 297-299.
  • Fronsdal C., Heidenreich W.F. Ann. Phys., 1992, 215(1), pp. 51-62.
  • Schmelzer I. General ether theory; 2000. ArXiv:gr-qc/0001101.
  • Arkani-Hamed N., Georgi H., Schwartz M.D. Ann. Phys., 2003, 305(2), pp. 96-118. ArXiv:hep-th/0210184.
  • Pitts J.B. Empirical equivalence, artificial gauge freedom and a generalized Kretschmann objection; 2009. ArXiv:0911.5400 [physics.hist-ph].
  • Pitts J.B. Class. Quantum Grav., 2017, 34(5), 055008(16pp). ArXiv:1609.04812 [gr-qc].
  • Pitts J.B. Found. Phys., 2018, 48(March), pp. 579-590. ArXiv.org:1803.10059 [physics.gen-ph].
  • Logunov A.A. The Relativistic Theory of Gravitation. New York: Nova Science, Commack; 1998. 183.
  • Babak S.V., Grishchuk L.P. Phys. Rev. D, 2000, 61(2), 24038(18pp). ArXiv:gr-qc/9907027.
  • Bambusi D., Grébert B. Duke Mathematical Journal, 2006, 135(3), pp. 507-567.
  • Weiland J., Wilhelmsson H. Coherent Non-linear Interaction of Waves in Plasmas. Oxford: Pergamon; 1977.
  • Petrov A.N. The field theoretical formulation of general relativity and gravity with non-zero masses of gravitons. Chapter in: Searches for a Mechanism of Gravity. Eds: Ivanov M.A., Savrov L.A. Nizhny Novgorod: Yu.Nickolaev; 2004, pp. 230-252. ArXiv:gr-qc/0505058.
  • Bergmann P.G., Thomson R. Phys. Rev., 1953, 89(2), pp. 400-407.
  • Goldberg J.N. Phys. Rev., 1958, 111(1), pp. 315-320.
  • Rosenfeld L. Sur le tenseur d'impulsion-énergie. English translation in: Selected Papers of Léon Rosenfeld. Eds: Cohen R.S., Stachel J.J. Dordrecht: D.Reidel; 1979, pp. 711-735.
  • Trautman A. Sov. Phys. Uspekhi, 1966, 9(3), pp. 319-339.
  • Van Dam H., Veltman M. Nucl. Phys. B, 1970, 22(2), pp. 397-411.
  • Tailor J.H. Rev. Mod. Phys., 1994, 66(3), pp. 711-720.
  • Chamseddine A.H., Mukhanov V. J. High En. Phys., 2013, 2013(3), 092(15pp). ArXiv:1302.4367 [hep-th]. 195. Volkov M.S. Phys. Rev. D, 2014, 90(2), 024028(6pp). ArXiv:1402.2953 [hep-th].
  • Deser S., Sandora M., Waldron A., Zahariade G. Phys. Rev. D, 2014, 90(10), 104043(13pp). ArXiv:1408.0561 [hep-th].
  • Deser S., Izumi K., and Ong Y.C., Waldron A. Mod. Phys. Lett. A, 2015, 30(3-4), 1540006(3pp). ArXiv:1410.2289 [hep-th].
  • Petrov A.N. Class. Quantum Grav., 2011, 28(21), 215021(17pp). ArXiv:1102.5636 [gr-qc].
  • Petrov A.N., Lompay R.R. Gen. Relat. Grav., 2013, 45(3), pp. 545-579. ArXiv:1211.3268 [gr-qc].
  • Zakharov V.I. JETP Lett., 1970, 12(9), pp. 312-314
  • Bergmann P.G. Phys. Rev., 1958, 112, pp. 287-289
  • Gupta S.N. Rev. Mod. Phys., 1957, 29(3), pp. 334-336
  • Pitts J.B. Gen. Relat. Grav., 2012, 44(February), pp. 401-426. ArXiv:1110.2077
  • Rosen N. Phys. Rev., 1940, 57(2), pp. 147-150
  • Brans C., Dicke R.H. Phys. Rev., 1961, 124(3), pp. 925-935
  • Gupta S.N. Phys. Rev., 1954, 96(6), pp, 1683-1685
  • Abbott L.F., Deser S. Nuclear Phys. B, 1982, 195(1), pp. 76-96. (1982)
  • Petrov A.N., Katz J. Proc. R. Soc. London A, 2002, 458(2018), pp. 319-337. ArXiv:gr-qc/9911025
  • Finkelstein D. Phys. Phys., 1958, 110(4), pp. 965-967
  • Fierz M., Pauli W. Proc. R. Soc. A, 1939, 173(953), pp. 211-232
  • Fierz M. Helvetica Physica Acta, 1940, 13(1), pp. 45-60
  • Babak S.V., Grishchuk L.P. Int. J. Mod. Phys. D, 2003, 12(10), pp. 1905-1959. ArXiv:gr-qc/0209006
  • Volkov M.S. Phys. Rev. D, 2014, 90(2), 024028(6pp). ArXiv:1402.2953 [hep-th]
  • Fierz M. Helvetica Physica Acta, 1940, 13(1), pp. 45-60
Еще
Статья обзорная
SciUp 2024 © 2024 ©