The theory of relativity and super-luminal-speeds

According to our Paper I (Cao Shenglin, 1988), it could be supposed that the physical space-time is a Finsler space-time, characterized by the metric ds ⁴=g _ijkf dx ⁱ dx ^j dx ^k dx ^f . If so, a new space-time transformation could be found by invariant ds ⁴ and the theory of relativity is discussed on this transformation.The project supported by National Natural Science Foundation of China.     

The theory of relativity and super-luminal-speeds (V)

In relation to some interesting subjects in the process of evolution of the universe, the nature of Finsler space-time and its cosmological implications are discussed. It is shown that the natures of the universal evolution could be attributed to the geometric features of the Finsler space-time. Based upon the theory of the singularities and bifurcation of caustics in the 3-dimensional space, galaxy formation and the large scale structure of the universe are also discussed. Electrons in the hot gas created by pancake shocks can upscatter photons in CBR, causing spectral distortions, and the largest scale of pancake limited by COBE observation would be 20 Mpc atz = 5, and 80 Mpc atz = 1.The project was supported by National Natural Science Foundation of China.     

The theory of relativity and super-luminal speeds

According to the different properties between the ds ² and the ds ⁴, it is discussed that the space-time will have the catastrophe nature on the Finsler metric ds ⁴ (see Cao, 1990, Paper II). The space-time transformations and the physical quantities will suddenly change at the catastrophe theory of the space-time. It will be supposed that only the dual velocity of the super-luminal-speed could be observed (see Cao, 1988). If so, a particle with the super-luminal-speedv>c, could be regarded as its anti-particle with the dual velocityv ₁=c ²/v<c.The project was supported by National Natural Science Foundation of China.     

Bellert's general relativity theory

In this paper, new ideas from our previous paper (Rydzyska, 1989)-i.e., problems connected with the new equivalence principle-have been developed. It is conformed, that certain static particles from Bellert's space-time are equivalent to a free particle from classic Milne's space-time. Mention is made of the algebraic structure of Bellert's space-time from (Rydzyska, 1990b). The space-time interval in this space-time, and its connection with a probability and the physical meaning of this interval and probability, has been defined. In the last section we derive dynamical equations for Bellert's space-time, i.e., we do the foundations of Bellert's general relativity theory.     

Cosmological considerations and the special theory of relativity

From the special theory of relativity it follows that the Universe is expanding during the expansive evolutionary phase with the limit velocity of the signal propagationc. The discovery of this fact throws a new light on a number of cosmological questions.     

New alternative for general relativity theory

This paper presents a scalar-tensor theory of gravitation with a flat background metric and an arbitrary coupling function. In what concerns PPN approximation as well as the speed and polarization of the weak gravitational wave, the suggested theory coincides with GR, while in the case of the strong field of gravitation it may considerably differ from GR.     

Static spherically-symmetric scalar-field theory in general relativity

A spherically-symmetric static scalar field in general relativity is considered. The field equations are defined by $$\begin{gathered} R_{ik} = - \mu \varphi _i \varphi _k ,\varphi _i = \frac{{\partial \varphi }}{{\partial x^i }}, \varphi ^i = g^{ik} \varphi _k , \hfill \\ \hfill \\ \end{gathered} $$ where ?=?(r,t) is a scalar field. In the past, the same problem was considered by Bergmann and Leipnik (1957) and Buchdahl (1959) with the assumption that ?=?(r) be independent oft and recently by Wyman (1981) with the assumption ?=?(r, t). The object of this paper is to give explicit results with a different approach and under a more general condition $$\phi _{;i}^i = ( - g)^{ - 1/2} \frac{\partial }{{\partial x^i }}\left[ {( - g)^{1/2} g^{ik} \frac{\partial }{{\partial x^k }}} \right] = - 4\pi ( -g )^{ - 1/2} \rho $$ where ?=?(r, t) is the mass or the charge density of the sources of the field.     

VariableG within a modified theory of general relativity

The case is made for modifying the equations of general relativity so as to permit a time-variable gravitational constant.     

Charged fluid sphere in bimetric general theory of relativity

Static and spherical symmetric solutions of the field equations in the bimetric general theory of gravitation are obtained for perfect and anisotropic charged fluids under the assumption that the physical metric admits a one-parameter group of conformal motion. All solutions are matched to the Reissner–Nordstrom metric and possess positive energy density larger than the stresses, everywhere within the sphere. The solution agrees with Einstein’s general relativity for a physical system comparable to the size of the universe, such as the solar system.     

The problem of motions up to the second post-newtonian approximation in general relativity theory

In this paper we give the Hamiltonian function for aN-body system up to the 2-P.N.A. Then as an example, from the LagrangianL _m of a test particle we derive the equations of its motion up to the 2-P.N.A. in the field of a heavy bodym ₂at rest.     

Equations of motion ofn massive-charged particles in general relativity theory

Starting with the Einstein-Maxwell field equations, we obtain the post-Newtonian equations of motion ofn massive-charged particles in general relativity.     

Anisotropic fluid distribution in higher dimensional general theory of relativity

We have obtained static and spherically symmetric self-gravitating solution of the field equations for anisotropic distribution of matter in higher- dimensional in the context of Einstein’s general theory of relativity. This work is an extension of the previous work of Hector Rago (Astrophys. Space Sci. 183:333, 1991) for four dimensional space-time. The solutions are matched to the analytical solutions for spherically symmetric self gravitating distribution of anisotropic matter obtained by Hector Rago (1991) for n=2.     

Bianchi type-III cosmological model in four- and five-dimensional bimetric theory of relativity

Four- and five-dimensional Bianchi type-III cosmological model in Rosen (1980) bimetric theory of gravitation is considered. Restricting to a particular type of background metric, it is observed that the Bianchi type-III cosmological model does not exist in case of both meson field and mesonic perfect fluid. Hence only vacuum model can be obtained.     

Bianchi Type-1 vacuum models in modified theory of general relativity

In this paper, the problem of spatially homogeneous and an isotropic Bianchi type-1 space time with perfect fluid distribution is considered in Barber's second theory of gravitation. To obtain determinate solutions, we have assumed the equation of statep= γρ, 0 ≤ γ ≤ 1. It is observed that the general fluid distribution degenerates isotropic vacuum model whenγ = 1 and Λ < 0. Further it is observed that the vacuum model obtained in case of γ = 0, ρ = 0 andΛ = 0, reduces to well known Kasner model in Einstein's theory. Some physical and geometrical aspects of the models together with singularities in the models are also discussed This revised version was published online in July 2006 with corrections to the Cover Date.     

Anisotropic spheres with uniform energy density in bimetric theory of relativity

In this paper we have obtained interior solutions of the field equations for anisotropic sphere in the bimetric general relativity theory formulated by Rosen (Lett. Nuovo Cimento 25, 1979). A class of solutions for a uniform energy-density source of the field equations is presented. The analytic solutions obtained are physically reasonable, well behaved in the interior of the sphere. The solutions agree with the Einstein’s general relativity for a physical system compared to the size of the universe such as the solar system.     

The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity

The classical Poisson equations of rotational motion are used to study the attitude motions of an Earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate Earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the Earth.A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Longterm solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.This paper represents a part of the author's Ph. D. dissertation for the Mathematics Department, Auburn University.     

Rotation of superfluid liquids in the framework of the general theory of relativity

Equations for the dynamics of a rotating two-component neutron star are derived in the framework of the general theory of relativity. The density of neutron vortex filaments is expressed in terms of the angular momentum density of the superfluid neutrons in the “npe” phase of the neutron star. It is shown that a theory of the relaxation of the angular velocity of pulsars must include corrections associated with the deviation of g₀₀ from unity, which is a consequence of the curvature of space.