Against Geometry: Nonstandard General Relativity


We show that the Schwarzschild solution can be embedded in a class of nonstandard solutions of the vacuum Einstein’s equations with arbitrary rotation curves. These nonstandard solutions have to be taken as physical, if dark matter as needed in the standard theory cannot be found. As a consequence general relativity is considered as a classical field theory in Minkowski space and not as a geometric theory in the sense of Einstein. Assuming an asymptotically flat rotation curve and introducing a material disk into this model we find a matter density in accordance with the Tully-Fisher relation.

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Scharf, G. (2015) Against Geometry: Nonstandard General Relativity. Open Access Library Journal, 2, 1-10. doi: 10.4236/oalib.1101389.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Poincaré, H. (1952) Science and Hypothesis. Dover Publications, Inc., New York.
[2] Xenon 100 Collaboration, 2012, arXiv 1207.5988
[3] Weinberg, S. (1972) Gravitation and Cosmology. John Wiley & Sons, Hoboken.
[4] Tully, R.B. and Fisher, J.R. (1977) A New Method of Determining Distances to Galaxies. Astronomy and Astrophysics, 54, 661-673.
[5] McGaugh, S.S., Schombert, J.M., Bothun, G.D. and de Blok, W.J.G. (2000) The Baryonic Tully-Fisher Relation. The Astrophysical Journal, 533, L99-L102.
[6] Scharf, G. (2011) Dark Matter in Galaxies According to the Tensor-Four-Scalars Theory. Physical Review D, 84, Article ID: 084045.
[7] Corbelli, E. (2003) Dark Matter and Visible Baryons in M33. Monthly Notices of the Royal Astronomical Society, 342, 199-207.
[8] Bräunlich, G. and Scharf, G. (2010) Gravitational Lensing and Rotation Curve. General Relativity and Gravitation, 43, 143-154.
[9] Taub, A.H. (1980) Space-Times with Distribution-Valued Curvature Tensors. Journal of Mathematical Physics, 21, 1423.
[10] Kuzmin, G.G. (1956) Astron. Zh., 33, 27
[11] Voigt, D. and Letelier, P.S. (2003) Exact General Relativistic Perfect Fluid Disks with Halos. Physical Review D, 68, Article ID: 084010.
[12] Scharf, G. (2012) Dark Matter in Galaxies According to the Tensor-Four-Scalars Theory III. arXiv 1205.4309.
[13] Milgrom, M. (1983) A Modification of the Newtonian Dynamics—Implications for Galaxy Systems. Astrophysical Journal, 270, 384.
[14] Scharf, G. (2012) Nonstandard General Relativity II. arXiv 1210.1496.
[15] Bekenstein, J.D. (2004) Revised Gravitation Theory for the Modified Newtonian Dynamics Paradigm. Physical Review D, 70, Article ID: 083509.

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