arXiv subjects
Publications and source records attributed to Merab Gogberashvili.
The model where the universe is considered as an expanding spherical 3-brane allows us to explain its expansion rate without a dark energy component. In this scenario the computed redshift that corresponds to the transition from cosmic deceleration to acceleration is in a good agreement with observations.
It is shown that a simple continuity condition in the algebra of split octonions suffices to formulate a system of differential equations that are equivalent to the standard Dirac equations. In our approach the particle mass and electro-magnetic potentials are part of an octonionic gradient function together with the space-time derivatives. As distinct from previous attempts to translate the Dirac equations into different number systems here the wave functions are real split octonions and not bi-spinors. To formulate positively defined probability amplitudes four different split octonions (transforming into each other by discrete transformations) are necessary, rather then two complex wave functions which correspond to particles and antiparticles in usual Dirac theory.
We examine the behavior of fermions in the presence of a non-singular thick brane having co-dimension 2. It is shown that one can obtain three trapped zero modes which differ from each other by having different values of angular momentum with respect to the 2 extra dimensions. These three zero modes are located at different points in the extra dimensional space and are interpreted as the three generations of fundamental fermions. The angular momentum in the extra dimensions (which is not conserved) acts as the family or generation label. This gives a higher dimensional picture for the family puzzle.
We show that the shell-universe model, used to explain the observed expansion rate of the universe without a dark energy component, provides also a natural mechanism for local increasing of the shell's tension leading to the modified Newton's law alternative to galactic dark matter.
We extend vector formalism by including it in the algebra of split octonions, which we treat as the universal algebra to describe physical signals. The new geometrical interpretation of the products of octonionic basis units is presented. Eight real parameters of octonions are interpreted as the space-time coordinates, momentum and energy. In our approach the two fundamental constants, $c$ and $\hbar$, have the geometrical meaning and appear from the condition of positive definiteness of the octonion norm. We connect the property of non-associativity with the time irreversibility and fundamental probabilities in physics.
A new solution to Einstein equations in (1+5)-spacetime with an embedded (1+3) brane is given. This solution localizes the zero modes of all kinds of matter fields and 4-gravity on the (1+3) brane by an increasing, transverse gravitational potential. This localization occurs despite the fact that the gravitational potential is not a decreasing exponential, and asymptotically approaches a finite value rather than zero.
We present a new (1+3)-brane solution to Einstein equations in (1+5)-space. As distinct from previous models this solution is free of singularities in the full 6-dimensional space-time. The gravitational potential transverse to the brane is an increasing (but not exponentially) function and asymptotically approaches a finite value. The solution localizes the zero modes of all kinds of matter fields and Newtonian gravity on the brane. An essential feature of the model is that different kind of matter fields have different localization radii.
A physical applicability of normed split-algebras, such as hyperbolic numbers, split-quaternions and split-octonions is considered. We argue that the observable geometry can be described by the algebra of split-octonions. In such a picture physical phenomena are described by the ordinary elements of chosen algebra, while zero divisors (the elements of split-algebras corresponding to zero norms) give raise the coordinatization of space- time. It turns to be possible that two fundamental constants (velocity of light and Planck constant) and uncertainty principle have geometrical meaning and appears from the condition of positive definiteness of norms. The property of non-associativity of octonions could correspond to the appearance of fundamental probabilities in four dimensions. Grassmann elements and a non-commutativity of space coordinates, which are widely used in various physical theories, appear naturally in our approach.
It is shown that Einstein's equations on the brane can be received from the multi-dimensional vector field equations in pseudo-Euclidean space. The idea is based on the observation that the brane geometry can be equivalently described by the intrinsic metric or by the derivatives of its normal. From the other hand the normal to the brane can be constructed with the components of some multi-dimensional vector fields. For the both cases 4-dimensional effective action for gravity appears to be the same.
In the framework of brane models the postulates of special relativity theory is revised. It is assumed that there exists preferred frame and relativity principle is violated on the brane. Because of trapping any moving object on the brane is really accelerated and the formulas for gravitational contraction of the intervals (containing the escape speed) appears to be equivalent to ordinary Lorentz ones.
Universe is considered as a brane in infinite (2+4)-space.It is shown that zero modes of all kinds of matter fields and 4-gravity are localized on the brane by increasing transversal gravitational potential.
Recently by us was proposed the model where Einstein's equation on the brane was connected with Maxwell's multi-dimensional equations in pseudo-Euclidean space. Based on this idea unification of 4-dimensional gravity and electromagnetism in (2+4)-space is found. In this picture photon is massless in four dimensions and obtains large mass in extra (1+1)-space normal to the brane.
Growing non-singular solution of 6-dimensional Einstein equations for the 4-brane in infinite transversal 2-space is found. This solution provides gravitational trapping of matter and 4-dimensional gravity on the brane without extra delta-like source. The suitable solution exists in the case of the (2+4)-space and not exists for the (1+5)-signature.
We consider the optical Sagnac effect, when the fictitious gravitational field simulates the reflections from the mirrors. It is shown that no contradiction exists between the conclusions of the laboratory and rotated observers. Because of acting of gravity-like Coriolis force the trajectories of co- and anti-rotating photons have different radii in the rotating reference frame, while in the case of the equal radius the effective gravitational potentials for the photons have to be different.
Brane-Universe model embedded in 6-dimensional space-time with the signature (2+4) is considered. A matter is gravitationally trapped in three space dimensions, but both time-like directions are open. Choosing of the dimension and the signature of the model is initiated with the conformal symmetry for massless particles and any point in our world can be (1+1) string-like object.
The solution of Einsteins equations for 4-brane embedded in 5-dimensional Anti-de-Sitter space-time is found. It is shown that the cosmological constant can provide the existence of ordinary 4-dimensional Newton's low and trapping of a matter on the brane.
Five dimensional model with extended dimensions investigated. It is shown that four dimensionality of our world is the result of stability requirement. Extra component of Einstein equations giving trapping solution for matter fields coincides with the one of conditions of stability.
In the model where the Universe is considered as a thin shell expanding in 5-dimensional hyper-space there is a possibility to have just one scale for a particle theory corresponding to the Universe thickness. From a realistic model the relation of this parameter to the Universe size was found.