MODERN THEORY OF GENERALISED RELATIVITY

We discuss various space-time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass. In this alternative cosmology the matter density was postulated to be a spatial delta function at the time of the big bang thereafter diffusing outward with constant total mass. This proposal explores a departure from standard assumptions that the big bang occurred everywhere at once or was just one of an infinite number of previous and later transitions.

2020

A constant 4 : 3 ratio of dimensions for contemporaneous spatial reference frames can account for expansion of the universe. In that case, space does not accelerate, cosmological inflation is unnecessary, the horizon problem does not exist and the cosmic constant a(t) does not vary with time. The underlying principles are based on dimensional capacity and its corollaries, the 4/3 law and contemporary reference frames, one three dimensional, the other four dimensional. Such a theory appears to be neutral as between a big bang or a steady state universe; the big bang is not a necessary implication of cosmological expansion.

For the collided region of two gravitationally bound structures A and B, geodesic equation is derived using calculus of variations. With the help of geodesic equation derived for the collided region of A and B, a method to calculate any possible curvature of universe beyond observable flat universe is detailed. This relativistic method is used to describe a generic idea on the evolution of gravitationally bound structures and its effect on the evolution of universe. Using this idea, distribution of matter and antimatter in the universe, observed accelerating expansion of universe, cosmic inflation, and large-scale structure of present universe are explained.

Physical review, 2021

In expanded universe, we found gravity field equation and solution. We found Schwarzschild solution, Kerr-Newman solution in expanded universe. Hence, We found new general relativity theory-Cosmological General Theory of Relativity(CGTR).

International Journal of Modern Physics A, 2009

We show how the curvature standard in Riemann's geometry can be fixed by Nash's theorem on locally embedded Riemannian geometries, which imply in the existence of extra dimensions. The resulting gravitational theory is more general than general relativity, similar to brane-world gravity, but where the propagation of the gravitational field along the extra dimensions is a mathematical necessity, rather than being a a postulate. After a brief introduction to Nash's theorem, we show that the vacuum energy density must remain confined to four-dimensional space-times, but the cosmological constant resulting from the contracted Bianchi identity is a gravitational contribution which propagates in the extra dimensions. Therefore, the comparison between the vacuum energy and the cosmological constant in general relativity ceases to be. Instead, the geometrical fix provided by Nash's theorem suggests that the vacuum energy density contributes to the perturbations of the gravitational field.

2004

A new cosmological theory is presented based on the proposition that all four metrical coefficients of space and time change with the cosmological expansion. Such a universal scale expansion would preserve the four-dimensional spacetime geometry and therefore by general relativity most physical relationships. In addition, if the scale expansion were exponential with time, all epochs would be equivalent. The theory resolves several outstanding problems with the Big Bang theory and better agrees with four observational programs. It also provides a simple explanation to the Pioneer anomaly.

International Journal of Theoretical Physics, 2012

In this paper, evolution of the high energy area of universe, through the scenario of 5 dimensional (5D) universe, has been studied. For this purpose, we solve Einstein equations for 5D metric and 5D perfect fluid to derive Fridmann-like equations. Then we obtain the evolution of scale factor and energy density with respect to both space-like and time-like extra dimensions. We obtain the novel equations for the space-like extra dimension and show that the matter with zero pressure cannot exist in the bulk. Also, for dark energy fluid and vacuum fluid, we have both accelerated expansion and contraction in the bulk.

Eprint Arxiv Physics 0606155, 2006

The third logically consistent and more rational space-time theory…..…………(4) 3. The Rationality Problems of the Principles of Equivalence and General Relativity...….…………………………......(13) 4. Singularities Appearing in the Gravitational Fields of Thin Circle and Double Spheres and the Rationality Problem of the Einstein's Equations of Gravitational Fields……………………………...……......(25) 5. Revised Formulas of Newtonian Gravity Based on the Schwarzschild Solution of the Einstein's Equation of Gravitation fields………….......(39) 6. The Gravitational Theory Established in Flat Space-time...…………..(62) 7. The Cosmological theory Established in Flat Space-time……………..(67) Authors who are not interested in the concept analysis of space-time and gravitation can start from Section 4 after reading introduction By the coordinate transformations of the Kerr and Kerr-Newman solutions, the solutions for the static distributions of mass thin loop and double spheres with axial symmetry are obtained. The results indicate that no matter what the masses and the densities of thin loop and double spheres are, the space's curvatures in the centre points of loop and the double sphere's connecting line are infinite. The singularity points are completely exposed in vacuum. The space curvatures nearby the singularity points and the surfaces of thin loop as well as double spheres are also highly curved even though the gravitational fields are very weak. It is obvious that all of them are actually impossible. The results show that the space-time singularities appearing in the Einstein's theory of gravity are not caused by the high density and huge mass's distributions. They are caused actually by the descriptive method of curved space-time, having nothing to do with the real world. After the geodesic equation described by the Schwarzschild solution of the Einstein's equation of gravitational field is transformed into flat reference frame to describe, all space-time singularities are transformed into the infinite points of gravitations. This kind of infinites would appear in all theories based on the mode of point particles and not worth to be surprise. So we should give up the descriptive method of geometry, retuning to the classical descriptive method of dynamics and interaction for gravitation.

Cosmological models can describe the physical universe, which shows that the universe expanding from the big bang.The expansion of space in homogeneous and isotropic models of the universe in the context of general relativity is Friedmann equations. Friedmann equation is the standard model in cosmology. The solutions of the Friedmann equations explain the flat, open and close universe. In this paper, we have attempted to present the Friedmann equation mathematically. We also demonstrated the process ofhow to solve our proposed equation easily.