General Relativity

The research on gravity theory focuses on problems, related to the implementation of new mathematical techniques and especially in relativistic reference systems, the theory of which is widely implemented and is of great importance for future astrophysical experiments such as GAIA and LISA. The problems treated are:

  1. Manoff’s generalized deviation equation and its possible applications in relativistic astrometry, celestial mechanics and Relativistic Reference Systems – geocentric and barycentric.
  2. Algebraic geometry approach in gravitational theory. New solutions of the Einstein’s equations in terms of elliptic functions within the framework of extended gravitational theories.
  3. Application of the algebraic geometry approach and of the anisotropic length scale in anisotropic cosmological models, also in isotropic cosmological models of the Friedman-Robertson-Walker type with the purpose of finding new solutions of the corresponding nonlinear equations.

References

  1. Bogdan G. Dimitrov, “Cubic algebraic equations in gravity theory, parametrization with the Weierstrass function and nonarithmetic theory of algebraic equations”, Journ. of Math. Phys. 44 (2003) 2542-2578.
  2. Bogdan G. Dimitrov, “Elliptic Curves, Algebraic Geometry Appoach in Gravity Theory And Uniformization Of Multivariable Cubic Algebraiс Equations“, Int. J. Geom. Meth. Mod. Phys. 5 (2008) 677-698.
  3. Bogdan G. Dimitrov, “Algebraic geometry approach in gravity theory and new relations between the parameters in type I low-energy string theory action in theories with extra dimensions”, Ann. Der Physik (Berlin) 19 № 3‐5 (2010) 254‐257.
  4. S.S. Manoff, and B. G. Dimitrov, “Flows and particles with shear-free and expansion-free velocities in (Ln, g)- and Weyl spaces”, Class. Quant. Grav. 19 (2002) 4377 – 4397.
  5. S.S. Manoff, and B. G. Dimitrov,” On the Existence of a Gyroscope in Spaces with Affine Connections and Metrics”, Gen. Rel. Gravit. 35 No.1 (2003) 25‐33.