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Spherically symmetric solutions in macroscopic gravity. (English) Zbl 1152.83337

Summary: Schwarzschild’s solution to the Einstein Field Equations was one of the first and most important solutions that lead to the understanding and important experimental tests of Einstein’s theory of General Relativity. However, Schwarzschild’s solution is essentially based on an ideal theory of gravitation, where all inhomogeneities are ignored. Therefore, any generalization of the Schwarzschild solution should take into account the effects of small perturbations that may be present in the gravitational field. The theory of Macroscopic Gravity characterizes the effects of the inhomogeneities through a non-perturbative and covariant averaging procedure. With similar assumptions on the geometry and matter content, a solution to the averaged field equations as dictated by Macroscopic Gravity are derived. The resulting solution provides a possible explanation for the flattening of galactic rotation curves, illustrating that Dark Matter is not real but may only be the result of averaging inhomogeneities in a spherically symmetric background.

MSC:

83C15 Exact solutions to problems in general relativity and gravitational theory
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)

Software:

GRTensorII
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[1] Will C.M. (1993). Theory and Experiment in Gravitational Physics (Revised Edition). Cambridge University Press, Cambridge · Zbl 0785.53068
[2] Perlmutter S. (1999). Astrophys. J. 517: 565 · Zbl 1368.85002 · doi:10.1086/307221
[3] Reiss A.G. (1998). Astrophys. J. 116: 1009
[4] Rubin V.C. (1983). Science 220: 1339 · doi:10.1126/science.220.4604.1339
[5] Rubin V.C., Ford W.K. and Thonnard N. (1980). Astrophys. J. 238: 471 · doi:10.1086/158003
[6] Rubin V.C., Ford W.K., Thonnard N. and Burstein D. (1982). Astrophys. J. 261: 439 · doi:10.1086/160355
[7] Rubin V.C., Burstein D., Ford W.K. and Thonnard N. (1985). Astrophys. J. 289: 81 · doi:10.1086/162866
[8] Sofue Y. and Rubin V.C. (2001). Ann. Revs. Astron. Astrophys. 39: 137 · doi:10.1146/annurev.astro.39.1.137
[9] Borriello A. and Salucci P. (2001). Mon. Not. Royal Astron. Soc. 323: 285 · doi:10.1046/j.1365-8711.2001.04077.x
[10] Persic M., Salucci P. and Stel F. (1996). Mon. Not. R. Astron. Soc. 281: 27
[11] Bergström L. (2000). Rep. Prog. Phys. 63: 793 · doi:10.1088/0034-4885/63/5/2r3
[12] Ostriker J.P. and Peebles P.J.E. (1973). Astrophys. J. 186: 467 · doi:10.1086/152513
[13] Tremaine S. (1992). Phys. Today 45: 28–36 · doi:10.1063/1.881329
[14] Ellis, G.F.R.: In: Bertotti, B., de Felice, F., Pascolini, A. (eds.) General Relativity and Gravitation, p. 215. Reidel, Dordrecht (1984)
[15] Ellis G.F.R. and Stoeger W. (1987). Class. Q. Grav. 4: 1697 · Zbl 0626.53071 · doi:10.1088/0264-9381/4/6/025
[16] Zalaletdinov R.M. (1992). Gen. Rel. Grav. 24: 1015–1031 · doi:10.1007/BF00756944
[17] Zalaletdinov R.M. (1993). Gen. Rel. Grav. 25: 673 · Zbl 0854.53067 · doi:10.1007/BF00756937
[18] Zalaletdinov R.M. (1997). Bull. Astron. Soc. India 25: 401
[19] Zalaletdinov, R.M.: Int. J Mod. Phys. A, to appear (2008), preprint arXiv:gr-qc/0801.3256
[20] Zalaletdinov, R.M.: Averaging Problem in Cosmology and Macroscopic Gravity. preprint arXiv:gr-qc/0701116
[21] Krasiński A. (1997). Inhomogeneous Cosmological Models. Cambridge University Press, Cambridge · Zbl 0997.83524
[22] Shirokov M.F. and Fisher I.Z. (1963). Sov. Astron. J. 6: 699
[23] Shirokov, M.F., Fisher, I.Z.: Gen. Rel. Grav. 30, 1411–1427 (1998) (Reprinted)
[24] Noonan T.W. (1984). Gen. Rel. Grav. 16: 1103 · doi:10.1007/BF00760648
[25] Noonan T.W. (1985). Gen. Rel. Grav. 17: 535 · doi:10.1007/BF00763047
[26] Isaacson R.A. (1968). Phys. Rev. 166: 1263 · doi:10.1103/PhysRev.166.1263
[27] Isaacson R.A. (1968). Phys. Rev. 166: 1272 · doi:10.1103/PhysRev.166.1272
[28] Futamase T. (1988). Phys. Rev. Lett. 61: 2175 · doi:10.1103/PhysRevLett.61.2175
[29] Futamase T. (1996). Phys. Rev. D 53: 681 · doi:10.1103/PhysRevD.53.681
[30] Bildhauer S. and Futamase T. (1991). Gen. Rel. Grav. 23: 1251–1264 · doi:10.1007/BF00756847
[31] Zotov N.V. and Stoeger W. (1992). Class. Q. Grav. 9: 1023 · doi:10.1088/0264-9381/9/4/017
[32] Kasai M. (1993). Phys. Rev. D 47: 3214 · doi:10.1103/PhysRevD.47.3214
[33] Boersma J.P. (1998). Phys. Rev. D 57: 798 · doi:10.1103/PhysRevD.57.798
[34] Buchert T. (2000). Gen. Rel. Grav. 32: 105–125 · Zbl 0976.83073 · doi:10.1023/A:1001800617177
[35] Buchert T. (2001). Gen. Rel. Grav. 33: 1381–1405 · Zbl 1020.83035 · doi:10.1023/A:1012061725841
[36] Paranjape A. and Singh T.P. (2007). Phys. Rev. D 76: 044006 · doi:10.1103/PhysRevD.76.044006
[37] Paranjape, A.: A Covariant Road to Spatial Averaging in Cosmology: Scalar Corrections to the Cosmological Equations. Preprint gr-qc/0705238 (2007) · Zbl 1153.83436
[38] Coley A.A., Pelavas N. and Zalaletdinov R.M. (2005). Phys. Rev. Lett. 95: 151102 · Zbl 1255.83136 · doi:10.1103/PhysRevLett.95.151102
[39] Coley A.A. and Pelavas N. (2006). Phys. Rev. D 74: 087301 · doi:10.1103/PhysRevD.74.087301
[40] Coley A.A. and Pelavas N. (2007). Phys. Rev. D 75: 043506 · doi:10.1103/PhysRevD.75.043506
[41] Plebański J. and Krasińki A. (2006). An Introduction to General Relativity and Cosmology. Cambridge University Press, Cambridge · Zbl 1103.83001
[42] van den Hoogen, R.J., Zalaletdinov, R.M.: (2006) [in preparation]
[43] Zalaletdinov, R.M.: private communication
[44] Hawking S.W. and Ellis G.F.R. (1973). The Large Scale Structure of Space-time. Cambridge University Press, Cambridge · Zbl 0265.53054
[45] Lake K. (2004). Phys. Rev. Lett. 92: 051101 · doi:10.1103/PhysRevLett.92.051101
[46] Bharadwaj S. and Kar S. (2003). Phys. Rev. D 68: 023516 · doi:10.1103/PhysRevD.68.023516
[47] Nucamendi U., Salgado M. and Sudarsky D. (2001). Phys. Rev. D 63: 125016 · doi:10.1103/PhysRevD.63.125016
[48] Zalaletdinov R. and Hoogen R.J. (2007). The MG Eqs Code [A computer algebra code for generation and manipulation with the equations of Macroscopic Gravity]. St. Francis Xavier University, Canada
[49] GRTensorII is a software package that runs within MAPLE. It is distributed freely at http://grtensor.org
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