The Theory of Gravitation in the Space - Time with Fractal Dimensions and Modified Lorents Transformations

Abstract

In the space and the time with a fractional dimensions the Lorents transformations fulfill only as a good approach and become exact only when dimensions are integer. So the principle of relativity (it is exact when dimensions are integer) may be treated also as a good approximation and may remain valid (but modified) in case of small fractional corrections to integer dimensions of time and space. In this paper presented the gravitation field theory in the fractal time and space (based on the fractal theory of time and space developed by author early). In the theory are taken into account the alteration of Lorents transformations for case including $v=c$ and are described the real gravitational fields with spin equal 2 in the fractal time defined on the Riemann or Minkowski measure carrier. In the theory introduced the new "quasi-spin", given four equations for gravitational fields (with different "quasi spins" and real and imaginary energies). For integer dimensions the theory coincide with Einstein GR or Logunov- Mestvirichvili gravitation theory.

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References in corpus (7)

• What Dimensions Do the Time and Space Have: Integer or Fractional?
• Generalized Riemann - Liouville fractional derivatives for multifractal sets
• Is it Possible to Transfer an Information with the Velocities Exceeding Speed of Light in Empty Space?
• Physical Consequences of Moving Faster than Light in Empty Space
• Multifractality of time and space, covariant derivatives and gauge invariance
• The Multifractal Time and Irreversibility in Dynamic Systems
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Cited by in corpus (6)

• Fractional Differential Forms
• Why We Can Not Walk To and Fro in Time as Do it in Space? (Why the Arrow of Time is Exists?)
• Do Gravitational and Electromagnetic Fields Have Rest Masses in the Fractal Universe?
• About Small Corrections to General Relativity: Gravitational Acceleration Depands of the Accelereted Bodies Masses
• Newton Equations May be Treated as Diffusion Equations in the Real Time and Space Fields of Multifractal Universe (Masses are Diffusion Coefficients of Diffusion-like Equations)
• How Much Energy Have Real Fields Time and Space in Multifractal Universe?