Anisotropic geometrodynamics: observations and cosmological consequences

1. Anisotropic geometrodynamics: observations and cosmological consequences Sergey Siparov State University of Civil Aviation, St-Petersburg Russian Federation “Gamov-2009”, Odessa

2. Motivation (observational) • Flat rotation curves of spiral galaxies – modern challenge: simple, not small, statistically verified – contradicts the theory!

3. Attempts to modify the gravitation theory in order to explain flat RC Einstein-Hilbert action • 1. f(R)-theories (De Witt) – where to stop? • 2. Additional scalar fields (Brans-Dicke) – still not found • 3. Weyl tensor (Mannheim) – no GW • 4. Scalar-vector-tensor theory (Moffat) – 5-th force (repulsive) • 5. Phenomenological MOND theory (Milgrem) – arbitrary choice of functions to fit observations • Dark matter notion – inconsistent Unsatisfactory 

4. Astrophysical (observational) restrictions for any gravitation theory modifications • 1. Flat rotation curves • 2. Tully-Fisher law for luminosity: • 3. Globular clusters behavior (I): no need for any correction to the gravitation law outside the spiral galaxy plane (anisotropy ?) • 4. Globular clusters behavior (II): contrary to the Keplerian expectations, they are found rather in the vicinity of the galaxy center than at the periphery • 5. Lensing effect appears to be 4-6 times larger than predicted None is explained by the classical GRT

5. Suggestion: try anisotropic metricReasons: • Geometry:theaccount for anisotropy is the natural generalization leading to the natural change in the “simplest scalar” in EH action Physics:1)velocity dependent gravitation is consistent with the equivalence principle: it is impossible to distinguish the inertial forces (e.g. Corolis!) from gravitational forces; 2)gravitational force must enter the metric • Introduce where γ_ij - Minkowski metric ε_ij(x,y) - small anisotropic perturbation - directional variable (tangent to trajectory of a probe) u(x) – vector field generating the anisotropy – characterizes the velocities of the distributed gravitation sources

6. Generalized geodesics and assumptions • Generalized geodesics • Assumptions Use two Einstein’s assumptions: 1. The components y2 , y3, y4 can be neglected in comparison with y1 which is equal to unity within the accuracy of the second order; • 2. The motion is slow, therefore, the time x1-derivative in the equations for geodesics can be neglected in comparison to the space x2-, x3-, and x4-derivatives; Add similar one: • 3. On the y-subspace of the phase space (x,y) the y1-derivative can be neglected in comparison to the y2-, y3-, and y4-derivatives.

7. Generalized geodesics • Generalized geodesics • Use assumptions  k=l=1 yk=yl=1 • Introduce new tensor: to obtain

8. Geometrical “Maxwell equations” • Anti-symmetric rank-2 tensor suffices: • Use designation: to get • Use designation: to get • Interpretation: charge q - electromagnetism charge m_g - gravitation

9. Force of gravitation • Equation of motion: • Newton force • Velocity dependent force (analogue: Coriolis (or Lorentz) force) • Third force

10. Predecessors – GRT corrections for a rotating body in an isotropic space-time • Gravitomagnetism: correction to the spherically symmetric mass gravity due to its rotation. Lense-Thirring: orbit precession. Later: clock effect; Sagnac effect; gravitomagnetic Stern-Gerlach effect; Gravity Probe B – confirmed theory within less than 10% accuracy • Frame-dragging Einstein – geodesics with 3 terms (includes rotational and linear frame-dragging, and inertial mass increase when other masses are nearby) • AGD difference:it is the1-st order theory in an anisotropic space-time

11. AGD applications – simplified model Attraction center plus circular contourwith current Pay attention to the known one-to-one correlation with Maxwell equations Effective parameters (R_eff, J, V_eff) can be taken from observations

12. AGD applications - I • Rotation curves (initial goal) Model gives: z = 0; b = r/R_eff = O(1)  B_z(r)  J/r def: J = C_2  q = m_g = m - Newton law - flat curve -

13. AGD applications - II • Tully-Fisher law Model: Luminosity:

14. AGD applications - III • Applicability region and regimes • Illustrative qualitative limit case (giant Black Hole in the center of a galaxy) For M = 10^11M_Sol a_C/a_N = 1 at r ~ 10^18 m v ~ 10^5 m/s Consistent with observations  no reason to expect Newton law

15. AGD applications - IV • Numerical modeling • 1) Quasi-precession, non-Keplerian behavior of globular clusters, and lensing problem • 2) Spiral arms

16. AGD qualitative results and general cosmological consequences • GRT results remained valid in its applicability region • Flat RC explained • Astrophysical restrictions sufficed • AGD applicability regions determined, limit case checked • Qualitative pictures obtained • Specific prediction: change in the OMPR effect conditions • No dark matter for galaxies needed  is it the same for galaxy clusters? • Gravitation ceased to be only attraction  can there be no dark energy of repulsion? • Hubble red shift  is it Universe expansion or gravitational red shift as it could be according to the observed amazingly fast tangent motion of quasars at the periphery of the visible Universe?

17. Thank you!  S.Siparov, arXiv [gr-qc]: 0809.1817 (2008)