Geodesic
Exact Relativistic Treatment of Stationary Counter-Rotating Dust Disks: Axis, Disk, and Limiting Cases
Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 3, pp. 418-431 Cet article a éte moissonné depuis la source Math-Net.Ru

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We continue to study the construction of explicit solutions of the stationary axisymmetric Einstein equations, interpretable as counterrotating disks of dust. We discuss the previously constructed class of solutions for disks with constant angular velocity and constant relative density. The metric for these space-times is given in terms of theta functions on a Riemann surface of genus two. We discuss the metric functions at the axis of symmetry and on the disk. Interesting limiting cases are the Newtonian, static, and ultrarelativistic limits (in the latter limit, the central red shift diverges). 
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     author = {C. Klein},
     title = {Exact {Relativistic} {Treatment} of {Stationary} {Counter-Rotating} {Dust} {Disks:} {Axis,} {Disk,} and {Limiting} {Cases}},
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C. Klein. Exact Relativistic Treatment of Stationary Counter-Rotating Dust Disks: Axis, Disk, and Limiting Cases. Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 3, pp. 418-431. http://geodesic.mathdoc.fr/item/TMF_2001_127_3_a8/

[1] F. J. Ernst, Phys. Rev., 167 (1968), 1175 | DOI

[2] D. Maison, Phys. Rev. Lett., 41 (1978), 521 | DOI | MR

[3] V. A. Belinskii, V. E. Zakharov, ZhETF, 75:6 (1978), 1955 | MR

[4] G. Neugebauer, J. Phys. A, 12 (1979), L67 | DOI | MR

[5] G. Neugebauer, R. Meinel, Astrophys. J. Lett., 414 (1993), L97 ; Phys. Rev. Lett., 73 (1994), 2166 ; 75 (1995), 3046 | DOI | DOI | DOI | MR | Zbl

[6] D. A. Korotkin, TMF, 77 (1988), 25 ; \defaultreftexts D. A. Korotkin, Commun. Math. Phys., 137 (1991), 383 ; Class. Q Grav., 10 (1993), 2587 | MR | DOI | MR | Zbl | DOI | MR | Zbl

[7] C. Klein, O. Richter, Phys. Rev. Lett., 79 (1997), 565 | DOI

[8] C. Klein, O. Richter, Phys. Rev. D, 58 (1998), CID 124018 | DOI | MR

[9] C. Klein, O. Richter, Phys. Rev. Lett., 83 (1999), 2884 | DOI

[10] C. Klein, Phys. Rev. D, submitted | MR

[11] D. Kramer i dr., Tochnye resheniya uravnenii Einshteina, Energoizdat, M., 1982 | MR

[12] J. Fay, Theta Functions on Riemann Surfaces, Lect. Notes Math., 352, Springer, New York, 1973 | DOI | MR | Zbl

[13] D. Korotkin, H. Nicolai, Nucl. Phys. B, 475 (1996), 397 | DOI | MR | Zbl

[14] D. Korotkin, V. Matveev, Solutions of Schlesinger system and Ernst equation in terms of theta-functions, E-print gr-qc/9810041 | MR

[15] A. Yamada, Kodai Math. J., 3 (1980), 114 | DOI | MR | Zbl

[16] R. Wald, General Relativity, Univ. Chicago Press, Chicago, 1984 | MR | Zbl

[17] J. M. Bardeen, R. V. Wagoner, Astrophys. J., 167 (1971), 359 | DOI | MR

[18] T. Morgan, L. Morgan, Phys. Rev., 183 (1969), 1097 | DOI

[19] D. Mamford, Lektsii o teta-funktsiyakh, Mir, M., 1988 | MR

[20] C. Klein, Class. Q Grav., 14 (1997), 2267 | DOI | MR | Zbl

[21] R. Meinel, The rigidly rotating disk of dust and its black hole limit, E-print gr-qc/9703077

[22] I. Hauser, F. Ernst, J. Math. Phys., 21 (1980), 1126 | DOI | MR

[23] E. D. Belokolos, A. I. Bobenko, V. Z. Enolskii, A. R. Its, V. B. Matveev, Algebro-Geometric Approach to Nonlinear Integrable Equations, Springer, Berlin, 1994