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Genesis of general relativity — A concise exposition

Wei-Tou Ni

School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, 516, Jun Gong Rd., Shanghai 200093, P. R. China

E-mail Address: weitou@gmail.com

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https://doi.org/10.1142/S0218271816300044Cited by:0 (Source: Crossref)

Abstract

This short exposition starts with a brief discussion of situation before the completion of special relativity (Le Verrier’s discovery of the Mercury perihelion advance anomaly, Michelson–Morley experiment, Eötvös experiment, Newcomb’s improved observation of Mercury perihelion advance, the proposals of various new gravity theories and the development of tensor analysis and differential geometry) and accounts for the main conceptual developments leading to the completion of the general relativity (CGR): gravity has finite velocity of propagation; energy also gravitates; Einstein proposed his equivalence principle and deduced the gravitational redshift; Minkowski formulated the special relativity in four-dimentional spacetime and derived the four-dimensional electromagnetic stress–energy tensor; Einstein derived the gravitational deflection from his equivalence principle; Laue extended Minkowski’s method of constructing electromagnetic stress-energy tensor to stressed bodies, dust and relativistic fluids; Abraham, Einstein, and Nordström proposed their versions of scalar theories of gravity in 1911–13; Einstein and Grossmann first used metric as the basic gravitational entity and proposed a “tensor” theory of gravity (the “Entwurf” theory, 1913); Einstein proposed a theory of gravity with Ricci tensor proportional to stress–energy tensor (1915); Einstein, based on 1913 Besso–Einstein collaboration, correctly derived the relativistic perihelion advance formula of his new theory which agreed with observation (1915); Hilbert discovered the Lagrangian for electromagnetic stress–energy tensor and the Lagrangian for the gravitational field (1915), and stated the Hilbert variational principle; Einstein equation of GR was proposed (1915); Einstein published his foundation paper (1916). Subsequent developments and applications in the next two years included Schwarzschild solution (1916), gravitational waves and the quadrupole formula of gravitational radiation (1916, 1918), cosmology and the proposal of cosmological constant (1917), de Sitter solution (1917), Lense–Thirring effect (1918).

This review is dedicated to the memory of my father Fu-Yuan Ni (1915.11.28–2016.03.24).

This paper is to be published also in the book “One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity”, edited by Wei-Tou Ni (World Scientific, Singapore, 2016).

Keywords:

PACS: 01.65.+g, 04.20-q, 04.80.Cc

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References

1. I. Newton, Philosophiae Naturalis Principia Mathematica (Streater, London, 1687). Crossref, Google Scholar
2. E. Whittaker, A History of the Theories of Aether and Electricity II. The Modern Theories (Philosophical Library, 1954; American Institute of Physics, 1987). Google Scholar
3. J. Kepler, Astronomia Nova de Motibus Stellae Martis (Prague, 1609); Harmonice Mundi (Linz, 1619). Google Scholar
4. C. Wilson, The great inequality of Jupiter and Saturn from Kepler to Laplace, Ph. D. thesis, St. John’s College, Annapolis, Maryland, January 10, 1984, www.docin.com/p-1627154943.html. Google Scholar
5. P. Moore, The Story of Astronomy, 5th rev. ed. (Grosset & Dunlap Publishing, New York, 1977). Google Scholar
6. U. J. J. Le Verrier, Theorie du mouvement de Mercure, Ann. Observ. imp. Paris (Mém.) 5 (1859) 1. ADS, Google Scholar
7. U. J. J. Le Verrier, Nouvelles recherches sur les mouvements des planètes, C. R. Acad. Sci. Paris 29 (1849); the English translation of the quote in the text is from Ref. 8. Google Scholar
8. N. T. Roseveare, Mercury’s Perihelion from Le Verrier to Einstein (Clarendon Press, Oxford, 1982). Google Scholar
9. S. Newcomb, Discussion and results of observations on transits of Mercury from 1677 to 1881, Astr. Pap. Am. Ephem. Naut. Alm. 1 (1882) 367. Google Scholar
10. I. I. Shapiro, Solar system tests of GR: Recent results and present plans in General Relativity and Gravitation: Proc. 12th Int. Conf. General Relativity and Gravitation, University of Colorado at Boulder, July 2–8, 1989, eds. N. Ashby, D. F. Bartlett and W. Wyss (Cambridge, Cambridge University Press, 1990), pp. 313–330. Google Scholar
11. W.-T. Ni, Solar-system tests of the relativistic gravity, in One Hundred Years of General Relativity: From Genesis and Foundations to Gravitational Waves, Cosmology and Quantum Gravity, Chap. 8, eds. by W.-T. Ni (World Scientific, Singapore, 2016); Int. J. Mod. Phys. D 25 (2016) 1630003. Google Scholar
12. A. A. Michelson and E. W. Morley, On the relative motion of the Earth and the luminiferous ether, Am. J. Sci. 34 (1887) 333. Crossref, ADS, Google Scholar
13. M. Nagel, S. R. Parker, E. V. Kovalchuk, P. L. Stanwix, J. G. Hartnett, E. N. Ivanov, A. Peters and M. E. Tobar, Direct terrestrial test of Lorentz symmetry in electrodynamics to 10 $^{- 18}$ $^{- 18}$ , Nat. Commun. 6 (2015) 8174. Crossref, Web of Science, ADS, Google Scholar
14. R. V. Eötvös, Math. Naturwiss. Ber. Ungarn 8 (1889) 65. Google Scholar
15. G. Galilei, Discorsi e Dimostriazioni Matematiche Intorno a due Muove Scienze (Elzevir, Leiden, 1638). Google Scholar
16. T. A. Wagner, S. Schlamminger, J. H. Gundlach and E. G. Adelberger, Torsion-balance tests of the weak equivalence principle, Class. Quantum Grav. 29 (2012) 184002. Crossref, Web of Science, ADS, Google Scholar
17. P. Touboul, M. Rodrigues, G. Métris and B. Tatry, MICROSCOPE, testing the equivalence principle in space, C. R. Acad. Sci. Ser. IV 2(9) (2001) 1271. Google Scholar
18. MICROSCOPE Collaboration, CNES ONERA cooperation first ultra-precise measurements from Microscope (September 27, 2016) https://presse.cnes.fr/en/cnes-onera-cooperation-first-ultra-precise-measurements-microscope. Google Scholar
19. W.-T. Ni, Equivalence principles, spacetime structure and the cosmic connection, in One Hundred Years of General Relativity: From Genesis and Foundations to Gravitational Waves, Cosmology and Quantum Gravity, Chap. 5, ed. W.-T. Ni (World Scientific, Singapore, 2016); Int. J. Mod. Phys. D 25 (2016) 1630002. Google Scholar
20. H. A. Lorentz, Kon. Neder. Akad. Wet. Amsterdam. Versl. Gewone Vergad. Wisen Natuurkd. Afd. 6 (1904) 809. ADS, Google Scholar
21. H. Poincaré, Bibl. Congr. Int. Philos. 3 (1900) 457. Google Scholar
22. H. Poincaré, La Science et l’ Hypothése (Flammarion, Paris, 1902) (in German); Science and Method (Dover Publications Inc., London, 1952). Google Scholar
23. H. Poincaré, L’état et l’avenir de la physique mathematique, Bull. Sci. Math. 28 (1904) 302; the English translation in the text is from Ref. 26. Google Scholar
24. H. Poincaré, Electricité et Optique: La Lumiére et les Théories Électrodynamiques (Gauthier-Villars, Paris, 1901). Google Scholar
25. V. Messager and C. Letellier, A genesis of special relativity, in One Hundred Years of General Relativity: From Genesis and Foundations to Gravitational Waves, Cosmology and Quantum Gravity, Chap. 1, ed. W.-T. Ni (World Scientific, Singapore, 2016); Int. J. Mod. Phys. D 25 (2015) 1530024. Google Scholar
26. C. Marchal, Sciences 97 (1997) 2. Web of Science, Google Scholar
27. H. Poincaré, Sur la dynamique de l’electron, C. R. Acad. Sci. 140 (1905) 1504. Google Scholar
28. A. Einstein, Zur elektrodynamik bewegter Körper [On the Electrodynamics of Moving Bodies], Ann. Phys. 17 (1905) 891. Crossref, ADS, Google Scholar
29. A. Einstein, Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? Ann. Phys. 18 (1905) 639. Crossref, ADS, Google Scholar
30. A. Einstein, Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie, Ann. Phys. 20 (1906) 627. Crossref, Google Scholar
31. M. Planck, Verh. Dtsch. Phys. Ges. 8 (1906) 136. Google Scholar
32. H. Minkowski, Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern, Königliche Gesellschaft der Wissenschaften zu Gttingen. Mathematisch-Physikalische Klasse. Nachrichten, pp. 53–111 (1908); this paper was read before the Academy on 21 December 1907; (English translation) The fundamental equations for electromagnetic processes in Moving bodies, translated from German by Meghnad Saha and Wikisource, Available at: http://en.wikisource.org/wiki/Translation:The_Fundamental_Equations_for_Electro. Google Scholar
33. B. Riemann, Über die Hypothesen welche der Geometrie zu Grunde liegen (On the hypotheses which underlie geometry), lecture at Göttingen (1854). Google Scholar
34. E. B. Christoffel, J. Math. 70 (1869) 241. Google Scholar
35. F. Klein, Programm zum Eintritt in die Philosophische Fakultät der Universität. zu Erlangen, Erlangen, A. Deichert (1872); Reprinted in 1893 in Math. Ann. 63, and in Klein’s Ges. Math. Abhandl. I, 460. Google Scholar
36. C. Niven, Trans. R. Soc. Edinburgh 27 (1874) 473. Crossref, Google Scholar
37. W. Thomson, Philos. Trans. 146 (1856) 481. Crossref, Google Scholar
38. W. J. M. Rankine, Philos. Trans. 146 (1856) 261. Crossref, Google Scholar
39. J. W. Gibbs, Vector Analysis (New Haven, 1881–1884), p. 57. Google Scholar
40. G. Ricci and T. Levi-Civita, Méthodes de calcul différentiel absolu et leurs applications, Math. Ann. 54 (1900) 125. Crossref, Google Scholar
41. H. Poincaré, Sur la dynamique de l’electron, Rend. Circ. Mat. Palermo 21 (1906) 129. Crossref, Google Scholar
42. M. Planck, Zur dynamik bewegter systeme, Sitz. K.-Preuss. Akad. Wiss. (1907) 542 (Specially at p. 544) (in German); On the dynamics of moving systems (1907) (in German); M. Planck, translated from German by Wikisource, Availabel at: https://en.wikisource.org/wiki/Translation:On_the_Dynamics_of_Moving_Systems. Google Scholar
43. A. Einstein, Uber das Relativitätprinzip und die aus demselben gezogenen Folgerungen̈, Jahrb. Radioakt. Elektron. 4 (1907) 411 (in German); Corrections by Einstein in Jahrb. Radioakt. Elektronik 5 (1908) 98; English translations by H. M. Schwartz in Am. J. Phys. 45 (1977) 811. Google Scholar
44. H. Minkowski, Raum und Zeit, Phys. Z. 10 (1909) 104 (in German); H. A. Lorentz, A. Einstein, H. Minkowski and H. Weyl, The Principle of Relativity, translated by W. Perrett and G. B. Jeffery (Dover, New York, 1952). Google Scholar
45. R. Hargreaves, Integral forms and their connection with physical equations, Camb. Philos. Trans. 21 (1908) 107. Google Scholar
46. H. Bateman, The transformation of the electrodynamical equations, Proc. Camb. Math. Soc., Ser. 2 8 (1910) 223. Crossref, Google Scholar
47. F. Kottler, Über die Raumzeitlinien der Minkowski’schen Weit, Sitz. Akad. Wiss. Wien, Math.-Naturw. Kl. Abt. IIa 121 (1912) 1688. Google Scholar
48. C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973). Google Scholar
49. K. Kuroda, W.-T. Ni and W.-P. Pan, Gravitational waves: Classification, methods of detection, sensitivities, and sources, in One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, Chap. 10, ed. W.-T. Ni (World Scientific, Singapore, 2016); Int. J. Mod. Phys. D 24 (2015) 1530031. Google Scholar
50. A. Einstein, Über den einfluß der Schwerkraft auf die Ausbreitung des Lichtes, Ann. Phys. 35 (1911) 898; translated “On the Influence of Gravitation on the Propagation of Light” in The collected papers of Albert Einstein, Vol. 3: The Swiss years: writings, 1909–1911 (Princeton University Press, Princeton, New Jersey, 1994), Anna Beck translator. Google Scholar
51. J. G. von Soldner, On the deviation of a light ray from its motion along a straight line through the attraction of a celestial body which it passes close by, Astronomishes Jahrbuch für das Jahr 1804 (C. F. E. Späthen, Berlin, 1801), pp. 161–172. Google Scholar
52. J. Earman and C. Glymour, Relativity and eclipses: The British eclipse expeditions of 1919 and their predecessors, in Historical Studies in the Physical Sciences, Vol. 11 (1980), pp. 49–88. Crossref, Google Scholar
53. F. Dyson, A. Eddington and C. Davidson, A determination of the deflection of light by the Sun’s gravitational field, from observations made at the total eclipse of May 29, 1919, Philos. Trans. R. Soc. 220A (1920) 291. Crossref, ADS, Google Scholar
54. M. von Laue, Zur Dynamik der Relativitätstheorie, Annalen der Physik 35 (1911) 524–542. Crossref, Google Scholar
55. M. von Laue, Das Relativitätsprinzip (Friedrich Vieweg und Sohn, 1911). Google Scholar
56. M. Abraham, Lincei Atti 20 (1911) 678. Google Scholar
57. A. Einstein, Ann. Phys. 38 (1912) 355, 443. Crossref, Google Scholar
58. G. Nordström, Relativitätsprinzip und Gravitation, Phys. Zeit. 13 (1912) 1126–1129. Google Scholar
59. G. Nordström, Zur Theorie der Gravitation vom Standpunkt der Relativitätsprinzip, Ann. Phys. 42 (1913) 533. Crossref, Google Scholar
60. G. Nordström, Die Fallgesetze und Planeten bewegung in der Relativitätstheorie, Ann. Phys. 43 (1914) 1101. Crossref, Google Scholar
61. W.-T. Ni, Theoretical frameworks for testing relativistic gravity, IV: A compendium of metric theories of gravity and their post-Newtonian limits, Astrophys. J. 176 (1972) 769. Crossref, Web of Science, ADS, Google Scholar
62. G. J. Whitrow and G. E. Morduch, Relativistic theories of gravitation, in Vistas in Astronomy, ed. A. Beer, Vol. 6 (Pergamon Press, Oxford, 1965), pp. 1–67. Crossref, Google Scholar
63. A. Einstein and A. D. Fokker, Ann. Phys. 44 (1914) 321. Crossref, Google Scholar
64. A. Einstein and M. Grossmann, Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation [Outline of a Generalized Theory of Relativity and of a Theory of Gravitation], Z. Math. Phys. 62 (1913) 225. Google Scholar
65. A. Einstein and M. Besso, Manuscript on the motion of the perihelion of Mercury (1913) 360, (in German), in The Collected Papers of Albert Einstein, Vol. 4: The Swiss Years: Writings, 1912–1914 Albert Einstein, eds. M. J. Klein, A. J. Kox, J. Renn and R. Schulmann (Princeton University Press, 1995), see also the editorial note on p. 344; available at http://press.princeton.edu/einstein/digital/. Google Scholar
66. A. Einstein, Die formale Grundlage der allgemeinen Relativitätstheorie, Sitz. ber. Akad. Wiss. 1914 (1914) 1030 (in German) The Collected Papers of Albert Einstein, Vol. 6: The Berlin Years: Writings, 1914–1917 Albert Einstein (English translation supplement), eds. by M. J. Klein, A. J. Kox, J. Renn and R. Schulmann (Princeton University Press, 1995), pp. 30–84; available at: http://press.princeton.edu/ einstein/digital/. Google Scholar
67. A. Einstein, Zür allgemeinen Relativitätstheorie, Sitzber. Preuss. Akad. Wiss. 1915 (1915) 778 (in German); in The Collected Papers of Albert Einstein, Vol. 6: The Berlin Years: Writings, 1914–1917 Albert Einstein (English translation supplement), eds. M. J. Klein, A. J. Kox, J. Renn and R. Schulmann (Princeton University Press, 1995), pp. 98–107; available at: http://press.princeton.edu/einstein/digital/. Google Scholar
68. A. Einstein, Zür allgemeinen Relativitätstheorie (Nachtrag), Sitz. ber. Preuss. Akad. Wiss. (1915) 799 (in German); in The Collected Papers of Albert Einstein, Vol. 6: The Berlin Years: Writings, 1914–1917 Albert Einstein (English translation supplement) pp. 108-110, eds. M. J. Klein, A. J. Kox, J. Renn and R. Schulmann (Princeton University Press, 1995); available at: http://press.princeton.edu/einstein/digital/. Google Scholar
69. A. Einstein, Erklärung der Perihelbewegung des Merkur aus allgemeinen Relativitätstheorie, Sitz. ber. Preuss. Akad. Wiss. (1915) 831 (in German); English translation in The Collected Papers of Albert Einstein, Vol. 6: The Berlin Years: Writings, 1914–1917 Albert Einstein (English translation supplement) eds. by M. J. Klein, A. J. Kox, J. Renn and R. Schulmann (Princeton University Press, 1995), pp. 112–116, available at: http://press.princeton.edu/einstein/digital/. Google Scholar
70. D. Hilbert, Die Grundlagen der Physik, K. Ges. Wiss. Gött. Nachr. Math.-Phys. K. (1915) 395. Google Scholar
71. A. Einstein, Die Feldgleichungen der Gravitation, Sitz. ber. Preuss. Akad. Wiss. (1915) 844 (in German); The Collected Papers of Albert Einstein, Vol. 6: The Berlin Years: Writings, 1914–1917 Albert Einstein (English translation supplement) eds. M. J. Klein, A. J. Kox, J. Renn and R. Schulmann (Princeton University Press, 1995) pp. 117–120, available at: http://press.princeton.edu/einstein/digital/. Google Scholar
72. A. Einstein, Die Grundlage der allgemeinen Relätivitatstheorie, Ann. Phys. 49 (1916) 769. Crossref, ADS, Google Scholar
73. A. Einstein, Näherungsweise Integration der Feldgleichungen der Gravitation, Sitz. ber Preuss. Akad. Wiss. (1916) 688 (in German) (translated by Alfred Engel) in The Collected Papers of Albert Einstein, Vol. 6: The Berlin Years: Writings, 1914–1917 (English translation supplement, Doc. 32 (Princeton University Press, 1997), pp. 201–210, Available at: http://einsteinpapers.press.princeton.edu/vol6-trans). Google Scholar
74. A. Einstein, Über Gravitationswellen, Sitz. ber. K. Preuss. Akad. Wiss. (1918) (in German) 154; (in German) (translated by Alfred Engel) in The Collected Papers of Albert Einstein, Vol. 7: The Berlin Years: Writings, 1918–1921 (English translation supplement, Doc. 1 On gravitational waves (Princeton University Press), pp. 9–27, Available at: http://einsteinpapers.press.princeton.edu/vol7-trans). Google Scholar
75. A. S. Eddington, The propagation of gravitational waves, Proc. R. Soc. Lond. A 102 (1922) 268. Crossref, ADS, Google Scholar
76. D. Kennefick, Traveling at the Speed of Thought: Einstein and the Quest for Gravitational Waves (Princeton University Press, Princeton, 2007). Crossref, Google Scholar
77. C.-M. Chen, J. M. Nester and W.-T. Ni, A brief history of gravitational wave research, Chin. J. Phys. (2016), Available at: http://dx.doi.org/10.1016/j.cjph.2016.10.014. Web of Science, Google Scholar
78. S. Carlip, D.-W. Chiou, W.-T. Ni and R. Woodard, Quantum gravity: A brief history of ideas and some prospects, in One Hundred Years of General Relativity: From Genesis and Foundations to Gravitational Waves, Cosmology and Quantum Gravity, ed. W.-T. Ni (World Scientific, Singapore, 2016); Int. J. Mod. Phys. D 25 (2015) 1530028. Google Scholar
79. K. Schwarzschild, “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie”, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften 7 (1916) 189–196; English Translation, S. Antoci and A. Loinger, “On the gravitational field of a mass point according to Einstein’s theory”, arXiv:physics/9905030. Google Scholar
80. C. Heinicke and F. W. Hehl, Schwarzschild and Kerr solutions of Einstein’s field equation: An introduction, in One Hundred Years of General Relativity: From Genesis and Foundations to Gravitational Waves, Cosmology and Quantum Gravity, Chap. 3, ed. W.-T. Ni (World Scientific, Singapore, 2016); Int. J. Mod. Phys. D 25 (2015) 1530006. Google Scholar
81. A. Einstein, Kosmologische Betrachtungen zur allgemeinen Relativitaetstheorie, Sitz. ber. K. Preuss. Akad. Wiss. Berlin 1 (1917) 142. Google Scholar
82. W. de Sitter, On the relativity of inertia: Remarks concerning Einstein’s latest hypothesis, Proc. Kon. Ned. Akad. Wet. 19 (1917) 1217. ADS, Google Scholar
83. W. de Sitter, The curvature of space, Proc. Kon. Ned. Akad. Wet. 20 (1917) 229. ADS, Google Scholar
84. W. de Sitter, Proc. Kon. Ned. Akad. Wet. 20 (1917) 1309. ADS, Google Scholar
85. W. de Sitter, Mon. Not. R. Astron. Soc. 78 (1917) 3. Crossref, ADS, Google Scholar
86. M. Bucher and W.-T. Ni, General relativity and cosmology, in One Hundred Years of General Relativity: From Genesis and Foundations to Gravitational Waves, Cosmology and Quantum Gravity, Chap. 13, ed. W.-T. Ni (World Scientific, Singapore, 2016); Int. J. Mod. Phys. D 24 (2015) 1530030. Google Scholar
87. M. Davis, Cosmic structure in One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, ed. W.-T. Ni (World Scientific, Singapore, 2016); Int. J. Mod. Phys. D 23 (2014) 1430011. Google Scholar
88. M. Bucher, Physics of the cosmic microwave background anisotropy, in One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, ed. W.-T. Ni (World Scientific, Singapore, 2016); Int. J. Mod. Phys. D 24 (2015) 1530004. Google Scholar
89. X. Meng, Y. Gao and Z. Han, SNe Ia as a cosmological probe, in One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, ed. W.-T. Ni (World Scientific, Singapore, 2016); Int. J. Mod. Phys. D 24 (2015) 1530029. Google Scholar
90. T. Futamase, Gravitational lensing in cosmology, in One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, ed. W.-T. Ni (World Scientific, Singapore, 2016); Int. J. Mod. Phys. D 24 (2015) 530011. Google Scholar
91. K. Sato and J. Yokoyama, Inflationary cosmology: First 30 $+$ $+$ Years, in One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, ed. W.-T. Ni (World Scientific, Singapore, 2016); Int. J. Mod. Phys. D 24 (2015) 1530025. Google Scholar
92. D. Chernoff and H. Tye, Inflation, string theory and cosmic strings, in One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, ed. W.-T. Ni (World Scientific, Singapore, 2016); Int. J. Mod. Phys. D 24(2015) 1530010. Google Scholar
93. Lense and H. Thirring, Phys. Z. 19 (1918) 156 (in German); Gen. Relativ. Gravit. 16 (1984) 712. Google Scholar
94. B. P. Abbott, LIGO Scientific and Virgo Collab., Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116 (2016) 061102. Crossref, Web of Science, ADS, Google Scholar
95. B. P. Abbott, LIGO Scientific and Virgo Collab., GW151226: Observation of gravitational waves from a 22-solar-mass binary black hole coalescence, Phys. Rev. Lett. 116 (2016) 241103. Crossref, Web of Science, ADS, Google Scholar