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1 - 100 Years of General Relativity

from Part One - Einstein's Triumph

Published online by Cambridge University Press:  05 June 2015

By
George F. R. Ellis
Edited by
Abhay Ashtekar ,
Beverly K. Berger ,
James Isenberg  and
Malcolm MacCallum
George F. R. Ellis
Affiliation:
University of Cape Town
Abhay Ashtekar
Affiliation:
Pennsylvania State University
Beverly K. Berger
Affiliation:
Formerly Program Director for Gravitational Physics, National Science Foundation
James Isenberg
Affiliation:
University of Oregon
Malcolm MacCallum
Affiliation:
University of Bristol
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Summary

This chapter aims to provide a broad historical overview of the major developments in General Relativity Theory (‘GR’) after the theory had been developed in its final form. It will not relate the well-documented story of the discovery of the theory by Albert Einstein, but rather will consider the spectacular growth of the subject as it developed into a mainstream branch of physics, high-energy astrophysics, and cosmology. Literally hundreds of exact solutions of the full non-linear field equations are now known, despite their complexity [1]. The most important ones are the Schwarzschild and Kerr solutions, determining the geometry of the solar system and of black holes (Section 1.2), and the Friedmann–Lemaître– Robertson–Walker solutions, which are basic to cosmology (Section 1.4). Perturbations of these solutions make them the key to astrophysical applications.

Rather than tracing a historical story, this chapter is structured in terms of key themes in the study and application of GR:

  1. The study of dynamic geometry (Section 1.1) through development of various technical tools, in particular the introduction of global methods, resulting in global existence and uniqueness theorems and singularity theorems.

  2. The study of the vacuum Schwarzschild solution and its application to the Solar system (Section 1.2), giving very accurate tests of general relativity, and underlying the crucial role of GR in the accuracy of useful GPS systems.

  3. The understanding of gravitational collapse and the nature of Black Holes (Section 1.3), with major applications in astrophysics, in particular as regards quasi-stellar objects and active galactic nuclei.

  4. The development of cosmological models (Section 1.4), providing the basis for our understandings of both the origin and evolution of the universe as a whole, and of structure formation within it.

  5. The study of gravitational lensing and its astronomical applications, including detection of dark matter (Section 1.5).

  6. Theoretical studies of gravitational waves, in particular resulting in major developments in numerical relativity (Section 1.6), and with development of gravitational wave observatories that have the potential to become an essential tool in precision cosmology.

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General Relativity and Gravitation
A Centennial Perspective
 , pp. 10 - 48
Publisher: Cambridge University Press
Print publication year: 2015

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References

[1] Stephani, H. et al. 2003. Exact solutions of Einstein's field equations, Second edition. Cambridge: Cambridge University Press. Corrected paperback reprint, 2009.Google Scholar
[2] Ferreira, P. G. 2014. The perfect theory: a century of geniuses and the battle over general relativity. London: Little, Brown.Google Scholar
[3] Einstein, A. 1915. Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.), 844–847.
[4] Misner, C. W., Thorne, K. S., and Wheeler, J. A. 1973. Gravitation. San Francisco, CA: W. H. Freeman and Co.
[5] Hawking, S. W., and Ellis, G. F. R. 1973. The large scale structure of space-time. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
[6] Wald, R. M. 1984. General relativity. Chicago, IL: University of Chicago Press.CrossRefGoogle Scholar
[7] Stephani, H. 1990. General relativity: an introduction to the theory of the gravitational field (2nd edition). Cambridge: Cambridge University Press.Google Scholar
[8] Synge, J. L., and Schild, A. 1949. Tensor calculus. Toronto: University of Toronto Press. Reprinted 1961.Google Scholar
[9] Schouten, E. 1954. Ricci calculus: an introduction to tensor analysis and its geometrical applications (2nd edition). Die Grundlehren der Mathematischen Wissenschaften, vol. X. Berlin: Springer.CrossRefGoogle Scholar
[10] Ellis, G. F. R., Maartens, R., and MacCallum, M. A. H. 2012. Relativistic cosmology. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
[11] Penrose, R., and Rindler, W. 1984. Spinors and space-time I: two-spinor calculus and relativistic fields. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
[12] Ellis, G. F. R. 1967. J. Math. Phys., 8, 1171–1194.CrossRef
[13] Ellis, G. F. R., and MacCallum, M. A. H. 1969. Commun. Math. Phys., 12, 108–141.CrossRef
[14] Thorne, K. S. 1980. Rev. Mod. Phys., 52, 299–340.
[15] Challinor, A., and Lasenby, A. 1999. Astrophys. J., 513, 1–22.CrossRef
[16] Lewis, A., Challinor, A., and Lasenby, A. 2000. Astrophys. J., 538, 473–476.CrossRef
[17] Synge, J. L. 1937. Proc. Lond. Math. Soc., 43, 376. Reprinted as Gen. Rel. Grav. 41, 2177 (2009).
[18] Ehlers, J. 1961. Akad. Wiss. Lit. Mainz, Abh. Math.-Nat. Kl., 11. English translation by G. F. R., Ellis and P. K. S., Dunsby, in Gen. Rel. Grav. 25, 1225–1266 (1993).
[19] Sachs, R. K. 1962. Proc. Roy. Soc. Lond. A, 270, 103–126.CrossRef
[20] Synge, J. L. 1934. Ann. Math., 35, 705–713. Reprinted as Gen. Rel. Grav. 41, 1206 (2009).
[21] Pirani, F. A. E. 1956. Acta. Phys. Polon., 15, 389. Reprinted as Gen. Rel. Grav. 41 1216 (2009).
[22] Pirani, F. A. E. 1957. Phys. Rev., 105, 1089.CrossRef
[23] Newman, E. T., and Penrose, R. 1962. J. Math. Phys., 3, 566.CrossRef
[24] Raychaudhuri, A. K. 1955. Phys. Rev., 98, 1123–1126 Reprinted as Gen. Rel. Grav. 32, 749 (2000).CrossRef
[25] Ellis, G. F. R. 1971. Relativistic cosmology. Pages 104-182 of: Sachs, R. K. (ed), General relativity and cosmology. Proceedings of the International School of Physics “Enrico Fermi”, vol. XLVII. New York and London: Academic Press. Reprinted as Gen. Rel. Grav. 41, 581–660 (2009).Google Scholar
[26] Maartens, R., and Bassett, B. A. C. C. 1998. Class. Quant. Grav., 15, 705–717.
[27] Petrov, A. Z. 1954. Scientific Proceedings of Kazan State University (named after V. I. Ulyanov-Lenin), Jubilee (1804-1954) Collection, 114, 55–69. Translation by J., Jezierski and M. A. H., MacCallum, with introduction by M. A. H., MacCallum, Gen. Rel. Grav. 32, 1661–1685 (2000).
[28] Penrose, R. 1960. Annals of Physics, 10, 171–201.CrossRef
[29] Israel, W. 1966. Nuovo Cim. B, 44, 1–14. Erratum: Nuovo Cim. B 48, 463 (1967).CrossRef
[30] Gödel, K. 1949. Rev. Mod. Phys., 21, 447–450. Reprinted as Gen. Rel. Grav. 32, 1409 (2000).
[31] Penrose, R. 1964. Conformal treatment of infinity. Pages 565-584 of: DeWitt, B., and Dewitt, C. (eds), Relativity, groups and topology. New York: Gordon and Breach. Reprinted as Gen. Rel. Grav. 43, 901–922 (2011).Google Scholar
[32] Tipler, F. J., Clarke, C. J. S., and Ellis, G. F. R. 1980. Singularities and horizons: a review article. Page 97 of: Held, A. (ed), General relativity and gravitation: one hundred years after the birth of Albert Einstein, vol. 2. New York: Plenum.Google Scholar
[33] Rindler, W. 1956. Mon. Not. Roy. Astr. Soc., 116, 662. Reprinted as Gen. Rel. Grav. 34, 133 (2002).CrossRef
[34] Stellmacher, K. 1938. Math. Ann., 115, 136–52. Reprinted as Gen. Rel. Grav. 42, 1769–1789 (2010).
[35] Rendall, A. D. 2005. Living Rev. Rel., 8, 6.CrossRef
[36] Arnowitt, R., Deser, S., and Misner, C. W. 1962. The dynamics of general relativity. Pages 227–265 of: Witten, L. (ed), Gravitation: an introduction to current research. NewYork and London: Wiley. Reprinted in Gen. Rel. Grav. 40, 1997 (2008).
[37] Penrose, R. 1965. Phys. Rev. Lett., 14, 579.CrossRef
[38] Hawking, S. W., and Penrose, R. 1970. Proc. R. Soc. Lond. A, 314, 529–548.CrossRef
[39] Curiel, E., and Bokulich, P. 2012. Singularities and black holes. In: Zalta, E. N. (ed), The Stanford encyclopedia ofphilosophy (Fall 2012 edition). Stanford, CA: Stanford.Google Scholar
[40] Will, C. M. 2006. Living Rev. Rel., 9.
[41] Will, C. M. 1979. The confrontation between gravitational theory and experiment. In: Hawking, S., and Israel, W. (eds), General relativity: an Einstein centenary survey. Cambridge: Cambridge University Press.Google Scholar
[42] Fromholz, P., Poisson, E., and Clifford, C. M. 2014. Amer. J. Phys., 82, 295.CrossRef
[43] Schwarzschild, K. 1916. Sitzungsber. Preuss. Akad. Wiss., 189–196. Reprinted as Gen. Rel. Grav. 35, 951 (2003).
[44] Ashby, N. 2003. Living Rev. Rel., 6, 1.CrossRef
[45] Will, C. M. 2011. Physics, 4, 43.CrossRef
[46] Breton, R. P. et al. 2008. Science, 321, 104–107.CrossRef
[47] Reissner, H. 1916. Annalen der Physik, 50, 106–120.
[48] Nordström, G. 1918. Proc. Kon. Ned. Akad. Wet., 20, 1238.
[49] Kottler, F. 1918. Annalen der Physik, 56, 410–461.
[50] Kerr, R. P. 1963. J. Math. Mech., 12, 33.
[51] Kerr, R. P., and Schild, A. 1965. A new class of vacuum solutions of the Einstein field equations. Pages 1-12 of: Atti del convegno sulla relatività generale: problemi dell'energia e onde gravitazionali. Florence: Edizioni G. Barbèra. Reprinted as Gen. Rel. Grav. 41, 2485–2499 (2009).Google Scholar
[52] Abdelqader, M., and Lake, K. 2013. Phys. Rev. D, 88, 064042.CrossRef
[53] Carter, B. 1968. Commun. Math. Phys., 10, 280–310.CrossRef
[54] Carter, B. 1973. Black hole equilibrium states, part I analytic and geometric properties of the Kerr solutions. Pages 61-124 of: deWitt, C., and deWitt, B. (eds), Black holes - les astres occlus. New York: Gordon and Breach. Reprinted as Gen. Rel. Grav. 41, 2874–2938 (2009).Google Scholar
[55] Eisenstaedt, J. 1982. Arch. Hist. Exact Sci., 27, 157–198.
[56] Eisenstaedt, J. 1987. Arch. Hist. Exact Sci., 37, 275–357.
[57] Eddington, A. S. 1924. Nature, 113, 192.CrossRef
[58] Kruskal, M. D. 1960. Phys. Rev., 119, 1743–1745CrossRef
[59] Boyer, R. H. 1969. Proc. R. Soc. Lond. A, 311, 245–252.CrossRef
[60] Carter, B. 1968. Phys. Rev., 174, 1559–1571
[61] Boyer, R. H., and Lindquist, R. W. 1967. J. Math. Phys., 8, 265.CrossRef
[62] Lake, K., and Roeder, R. C. 1977. Phys. Rev. D, 15, 3513–3519.CrossRef
[63] Tolman, R. 1934. Proc. Nat. Acad. Sci., 20, 169. Reprinted in Gen. Rel. Grav., 29, 935-943 (1997).CrossRef
[64] Bondi, H. 1947. Mon. Not. Roy. Astr. Soc., 107, 410. Reprinted as Gen. Rel. Grav. 31, 1777–1781 (1999).CrossRef
[65] Krasński, A. 2006. Inhomogeneous cosmological models (2nd edition). Cambridge: Cambridge University Press.Google Scholar
[66] Begelman, M., and Rees, M. J. 2010. Gravity's fatal attraction: black holes in the Universe. Cambridge: Cambridge University Press.Google Scholar
[67] Oppenheimer, J. R., and Snyder, H. 1939. Phys. Rev., 56, 455–459.
[68] Israel, W. 1968. Commun. Math. Phys., 8, 245–260.CrossRef
[69] Penrose, R. 1999. J. Astrophys. Astr., 17, 213–231.
[70] Robinson, D. C. 1975. Phys. Rev. Lett., 34, 905–906.
[71]Bardeen, J. M., Carter, B., and Hawking, S. W. 1973. Commun. Math. Phys., 31, 161–170.CrossRef
[72] Abramowicz, M. A., and Fragile, P. C. 2013. Living Rev. Rel., 16, 1.CrossRef
[73] Rees, M. J. 1984. Ann. Rev. of Astron. Astrophys., 22, 471–506.CrossRef
[74] Ferrarese, L., and Merritt, D. 2002. Phys. World, 15(6), 41–46.CrossRef
[75] Penrose, R. 1996. J. Astrophys. Astr., 17, 213–231.CrossRef
[76] Celotti, A., Miller, J. C., and Sciama, D. W. 1999. Class. Quant. Grav., 16, A3–A21.CrossRef
[77] Schödel, R. et al. 2002. Nature, 419, 694–696.CrossRef
[78] Melia, F. 2007. The Galactic supermassive black hole. >Princeton, NJ: Princeton University Press.Google Scholar
[79] Einstein, A. 1917. Sitzungsber. Preuss. Akad. Wiss., 142–152. English translation in The principle ofrelativity by H. A., LorentzA., EinsteiH., Minkowski and H., Weyl (Dover: New York) 1923.Google Scholar
[80] Friedmann, A. 1922. Z. Phys., 10, 377–386. Reprinted as Gen. Rel. Grav. 31, 1991 (1999).CrossRef
[81] Friedmann, A. 1924. Z. Phys., 21, 326–332. Reprinted as Gen. Rel. Grav. 31, 12 (1999).CrossRef
[82] Lemaître, G. 1931. Nature, 127, 706.CrossRef
[83] Lemaître, G. 1933. C. R. Acad. Sci. Paris, 196, 1085.
[84] Ellis, G. F. R. 1990. Innovation, resistance and change: the transition to the expanding universe. Pages 97–114 of: Bertotti, B., Balbinot, R., Bergia, S., and Messina, A. (eds), Modern cosmology in retrospect. Cambridge: Cambridge University Press.Google Scholar
[85] Robertson, H. P. 1933. Rev. Mod. Phys., 5, 62–90. Reprinted as Gen. Rel. Grav. 44, 2115–2144 (2012).CrossRef
[86] Dodelson, S. 2003. Modern cosmology: anisotropies and inhomogeneities in the Universe. Amsterdam: Academic Press.Google Scholar
[87] Peter, P., and Uzan, J. P. 2013. Primordial cosmology. Oxford Graduate Texts. Oxford: Oxford University Press.Google Scholar
[88] Einstein, A. 1918. Sitzungsber. Preuss. Akad. Wiss., 154–167.
[89] Ehlers, J., and Rindler, W. 1989. Mon. Not. Roy. Astr. Soc., 238, 503–521.CrossRef
[90] Wainwright, J., and Ellis, G. F. R. 1997. Dynamical systems in cosmology. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
[91] Kristian, J., and Sachs, R. K. 1966. Astrophys. J., 143, 379–399.CrossRef
[92] Etherington, I. M. H. 1933. Phil. Mag., 15, 761. Reprinted as Gen. Rel. Grav. 39, 1055 (2007).CrossRef
[93] Sandage, A. 1961. Astrophys. J., 133, 355–392.CrossRef
[94] Ellis, G. F. R., and Rothman, T. 1993. Amer. J. Phys., 61, 883–893.CrossRef
[95] Wagoner, R. V., Fowler, W. A., and Hoyle, F. 1967. Astrophys. J., 148, 3–50.CrossRef
[96] Sunyaev, R. A., and Zel'dovich, Ya. B. 1970. Astrophys. Space Sci., 7, 21–30.
[97] Longair, M. 2013. The cosmic century. Cambridge: Cambridge University Press.
[98] Doreshkevich, A., Zel'dovich, Ya. B., and Novikov, I. D. 1967. Sov. Astron. AJ, 11, 233–239. Translated from Astronomicheskii Zhurnal 44, 295–303.
[99] Peebles, P. J. E. 1966. Astrophys. J., 146, 542–552.CrossRef
[100] Beringer, J. et al. [Particle Data Group]. 2012. Phys. Rev. D, 86, 010001.CrossRef
[101] Martin, J., Ringeval, C., and Vennin, V. 2013. Encyclopaedia inflationaris. arXiv: 1303.3787.
[102] Ellis, G. F. R., and Madsen, M. 1991. Class. Quant. Grav., 8, 667–676.CrossRef
[103] Lidsey, J. E. et al. 1997. Rev. Mod. Phys., 69, 373–410.CrossRef
[104] Peebles, P. J. E., and Yu, J. T. 1970. Astrophys. J., 162, 815.CrossRef
[105] Peebles, P. J. E. 1980. The large-scale structure ofthe Universe. Princeton, NJ: Princeton University Press.Google Scholar
[106] Lemaître, G. 1933. Ann. Soc. Sci. Bruxelles A, 53, 51. Translation by M.A.H., MacCalluminGen. Rel. Grav., 29, 641–680 (1997).
[107] Lemaître, G. 1949. Rev. Mod. Phys., 21, 357.CrossRef
[108] Lemaître, G. 1958. Pontifical Acad. Sci., Scripta Varia, 16, 475–488.
[109] Lifshitz, E. M. 1946. Acad. Sci. USSR J. Phys., 10, 116.
[110] Sachs, R. K., and Wolfe, A. M. 1967. Astrophys. J., 147, 73. Reprinted as Gen. Rel. Grav. 39, 1944 (2007).CrossRef
[111] Bardeen, J. M. 1980. Phys. Rev. D, 22, 1882–1905CrossRef
[112] Mukhanov, V. F., Feldman, H. A., and Brandenberger, R. H. 1992. Phys. Reports, 215, 203–333.CrossRef
[113] Kodama, H., and Sasaki, M. 1984. Prog. Theor. Phys. Suppl., 78, 1–166.CrossRef
[114] Hawking, S. W. 1966. Astrophys. J., 145, 544–554.CrossRef
[115] Ellis, G. F. R., and Bruni, M. 1989. Phys.Rev. D, 40, 1804–1818.
[116] Bruni, M., Dunsby, P. K. S., and Ellis, G. F. R. 1992. Astrophys. J., 395, 34–53.CrossRef
[117] Mukhanov, V. F. 2005. Physical foundations ofcosmology. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
[118] Lahav, O., Lilje, P. B., Primack, J. R., and Rees, M. J. 1991. Mon. Not. Roy. Astr. Soc., 251, 128–136.CrossRef
[119] Sakharov, A. D. 1965. Zh. Eksp. Teor. Fiz., 49, 345–358. Translated as Sov. Phys. JETP 22, 241-249 (1966).
[120] Sunyaev, R. A., and Zel'dovich, Ya. B. 1970. Astrophys. Space Sci., 7, 3.
[121] Sunyaev, R. A., and Zel'dovich, Ya. B. 1980. Ann. Rev. Astron. Astrophys., 18, 537–560.CrossRef
[122] Silk, J., and Wilson, M. L. 1979. Astrophys. J., 228, 641–646.CrossRef
[123] Bond, J. R., and Efstathiou, G. 1984. Astrophys. J. Lett., 285, L45–L48.CrossRef
[124] Efstathiou, G., Sutherland, W. J., and Maddox, S. J. 1990. Nature, 348, 705–707.CrossRef
[125] Bonnor, W. B. 1956. Z. Astrophys., 39, 143. Reprinted as Gen. Rel. Grav. 30, 1113–1132 (1998).
[126] Mustapha, N., Hellaby, C. W., and Ellis, G. F. R. 1999. Mon. Not. Roy. Astr. Soc., 292, 817–830.
[127] Misner, C. W. 1969. Phys. Rev. Lett., 22, 1071–1074CrossRef
[128] Lifshitz, E. M., and Khalatnikov, I. M. 1964. Sov. Phys. Usp., 6, 495–522.CrossRef
[129] Renn, J., Sauer, T., and Stachel, J. 1997. Science, 275, 184–186.CrossRefPubMed
[130] Einstein, A. 1936. Science, 84, 506–7.CrossRef
[131] Schneider, P., Ehlers, J., and Falco, E. E. 1992. Gravitational lenses. New York: Springer-Verlag.
[132] Wambsganss, J. 2001. Living Rev. Rel., 1, 12.CrossRef
[133]Blandford, R. D., and Narayan, R. 1992. Ann. Rev. Astron. Astrophys., 30, 311–358.CrossRef
[134] Perlick, V. 2004. Living Rev. Rel., 7, 9.CrossRef
[135] Einstein, A., and Rosen, N. J. 1937. J. Franklin Inst., 223, 43.CrossRef
[136] Bondi, H., Pirani, F. A. E., and Robinson, I. 1959. Proc. Roy. Soc. Lond. A, 251, 519–533.CrossRef
[137] Penrose, R. 1965. Rev. Mod. Phys., 37, 215.CrossRef
[138] Szekeres, P. 1972. J. Math. Phys., 13, 286–294.CrossRef
[139] Bondi, H., van der Burg, M. G. J., and Metzner, A. W. K. 1962. Proc. Roy. Soc. Lond. A, 269, 21.
[140] Schoen, R., and Yau, S.T. 1979. Commun. Math. Phys., 65, 45–76.CrossRef
[141] Witten, E. 1981. Commun. Math. Phys., 80, 381–402.CrossRef
[142] Teukolsky, S. A. 1973. Astrophys. J., 185, 635–648.CrossRef
[143] Sasaki, M., and Tagoshi, H. 2003. Living Rev. Rel., 6, 6.
[144] Kokkotas, K. D., and Schmidt, B. 1999. Living Rev. Rel., 2, 2.CrossRef
[145] Fryer, C. L., and New, K. C. B. 2011. Living Rev. Rel., 14, 1.CrossRef
[146] Blanchet, L. 2006. Living Rev. Rel., 9, 4.CrossRef
[147] Owen, R. et al. 2011. Phys. Rev. Lett., 106, 151101.CrossRef
[148] Nichols, D. A. et al. 2011. Phys. Rev. D, 84, 124014.CrossRef
[149] Zhang, F. et al. 2012. Phys. Rev. D, 86, 084049.CrossRef
[150] Nichols, D. A. et al. 2012. Phys. Rev. D, 86, 104028.CrossRef
[151] Taylor, J. H., Fowler, L. A., and McCulloch, P. M. 1979. Nature, 277, 437–440.
[152] Taylor, J. H., and Weisberg, J. M. 1989. Astrophys. J., 345, 434–450.CrossRef
[153] Turner, M. S., White, M. J., and Lidsey, J. E. 1993. Phys. Rev. D, 48, 4613–4622
[154] Turner, M. S. 1996. Phys. Rev. D, 55, 435–439.
[155] Martin, J., Ringeval, C., Trotta, R., and Vennin, V., 2014. Phys. Rev. D, 90, 063501.CrossRef
[156] Krauss, L. M., Dodelson, S., and Meyer, S. 2010. Science, 328, 989–992.CrossRef
[157] Sathyaprakash, B. S., and Schutz, B. F. 2009. Living Rev. Rel., 12, 2.CrossRef
[158] Kuroyanagi, S., Gordon, C., Silk, J., and Sugiyama, N. 2010. Phys. Rev. D, 81, 083524.CrossRef
[159] Lovelock, D. 1971. J. Math. Phys., 12, 498.CrossRef
[160] Weinberg, S. 1989. Rev. Mod. Phys., 61, 1–23.CrossRef

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