Induced antigravity in extended general relativity

Y.A. Rylov1


An extension of general relativity to non-Riemannian geometries suitable for description of the space-time geometry leads to integral dynamic equations which are valid for continuous and discrete space-times. The gravitational field of a homogeneous heavy non-rotating sphere is calculated inside the sphere. The space-time geometry appears to be non-Riemannian. In the case where the gravitational radius of the sphere is of the order of its own radius, an induced antigravity appears inside the sphere. In other words, the gravitational force inside the sphere appears to be directed from the center. The antigravity resists to a collapse of the sphere and to black hole formation.


  1. Yu. A. Rylov, Necessity of the general relativity revision and free motion of particles in non-Riemannian space-time geometry. Arxiv: 1001.5362.
  2. Yu. A. Rylov, Non-Euclidean method of the generalized geometry construction and its application to space-time geometry, in: Pure and Applied Differential Geometry eds. Franki Dillen and Ignace Van de Woestyne (Shaker Verlag, Aachen, 2007), pp. 238-246. See also Arxiv: Math.GM/0702552.
  3. Yu. A. Rylov, Geometry without topology as a new conception of geometry, Int. J. Mat. & Mat. Sci. 30 (12), 733-760 (2002),
  4. Yu. A. Rylov, General relativity extended to non-Riemannian space-time geometry, Arxiv: 0910.3582.
  5. J. L. Synge, Relativity: the General Theory (Amsterdam, North-Holland Publishing Company, 1960).
  6. Yu. A. Rylov, On a possibility of the Riemannian space description in terms of a finite interval. Izv. Vuzov, Matematika, No.3 (28), 131-142 (1962).
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