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.     

Comment to a paper of M. Villata on antigravity

In a recent paper of M. Villata, it is claimed that “antigravity appears as a prediction of general relativity when CPT is applied.” However, the present paper argues that Villata puts the cart before the horse qua methodology, and that the resulting theory cannot be reconciled with the ontological presuppositions of general relativity. The conclusion is that Villata’s suggestion for the physics that might underlie a gravitational repulsion of matter and antimatter is not acceptable as a fundamental theory in its current state of development.     

The model of a flat (Euclidean) expansive homogeneous and isotropic relativistic universe in the light of the general relativity,quantum mechanics,and observations

Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial solutions: Einstein special theory of relativity and Newton gravitation theory), quantum mechanics, and observations, too.     

Three classical tests of Hořava-Lifshitz gravity theory

Recently, a renormalizable gravity theory has been proposed by Hořava, and it might be an ultraviolet completion of general relativity or its infrared modification. Particular limit of the theory allows for the Minkowski vacuum. A spherical asymptotically flat black hole solution that represents the analogy of Schwarzschild solution of general relativity has been obtained. It will be very interesting to find the difference between traditional general relativity and Hořava-Lifshitz gravity theory. The three classical tests of general relativity including gravitational red-shift, perihelion precession of the planet Mercury, and light deflection in gravitational field in the spherical asymptotically flat black hole solution of infrared modified Hořava-Lifshitz gravity are investigated. The first order corrections from the standard general relativity is obtained. The result can be used to limit the parameters in Hořava-Lifshitz gravity and to show the viability of the theory.     

A Study Of Global Monopole In Einstein–Cartan Theory

The gravitational field of a global monopole in the context of Einstein–Cartan theory is investigated. A comparison is made with the corresponding results predicted by general relativity. PACS Nos: 98.80cq; 04.20 jb; 04.50     

Torsion,minimum time,string tension and its physical implications in cosmology

We show that introducing torsion in general relativity, that is, physically, considering the effect of the spin, and linking the torsion to defects in the space-time topology we can have a minimum unit of time. In this context we have the possibility of identifying the defects in space-time topology induced by torsion as behaving like a string so that the minimum length, derived by treating the spin as an extra dimension, is related with string tension. Physical implications are considered for field theory (we can eliminate the divergence of self-energy integral without introducing anyad hoc cut-off), particle decay, evaporation of black holes, and information theory.     

On the viability of a certain vector-tensor theory of gravitation

A certain vector-tensor theory is revisited. Our attention is focused on cosmology. Against previous suggestions based on preliminary studies, it is shown that, if the energy density of the vector field is large enough to play the role of the dark energy and its fluctuations are negligible, the theory is not simultaneously compatible with current observations on: supernovae, the cosmic microwave background (CMB) anisotropy, and the power spectrum of the energy density fluctuations. However, for small enough energy densities of the vector field and no scalar fluctuations, the theory becomes compatible with all the above observations and, moreover, it leads to an interesting evolution of the so-called vector cosmological modes. This evolution appears to be different from that of general relativity, and the difference might be useful to explain the anomalies in the low order CMB multipoles.     

Energy release on the surface of a rapidly rotating neutron star during disk accretion: A thermodynamic approach

The total energy E of a star as a function of its angular momentum J and mass M in the Newtonian theory, E=E(J, M) [in general relativity, the gravitational mass of a star as a function of its angular momentum J and rest mass m, M=M(J, m)], is used to determine the remaining parameters (angular velocity, chemical potential, etc.) in the case of rigid rotation. Expressions are derived for the energy release during accretion onto a cool (with constant entropy), rapidly rotating neutron star (NS) in the Newtonian theory and in general relativity. A separate analysis is performed for the cases where the NS equatorial radius is larger and smaller than the radius of the marginally stable orbit in the disk plane. An approximate formula is proposed for the NS equatorial radius for an arbitrary equation of state, which matches the exact equation of state at J=0.     

Mathematical theory of the origin of matter

It is shown that from a simple and elegant action it is possible to obtain: (i) the equations of classical dynamics, (ii) Schrödinger's equation, (iii) the dynamical equation of special relativity, (iv) scale-invariant gravitation including general relativity, (v) the mathematical theory of the origin of matter, and (vi) the potential function of inflationary theory.When the action term in question is related to the electromagnetic theory an ugly feature arises, however. There must be a multiplication by a small dimensionless number of order 10^–38. If this ugly feature is to be avoided, matter must be taken to originate, not as particles observed in the laboratory but as Planck particles. The decay of each such particle into 10¹⁹ hadrons then explains the genesis of numbers of order 10³⁸ that appear in physics and cosmology. It also raises questions concerning primordial nucleosynthesis which were discussed in the preceding paper.     

黑洞吸积盘的演化及温度分布的热不稳定性

本文在Ｔｈｏｒｎｅ工作的基础上讨论了吸积盘中黑洞的有关参量的演化，以及由Ｓｃｈｗａｒｚｓｃｈｉｌｄ黑洞吸积盘向Ｋｅｒｒ黑洞吸积盘演化过程中对吸积盘辐射通量的影响，最后针对几个典型的辐射过程，分别讨论了黑洞吸积盘在牛顿框架中的温度分布方程与广义相对论的温度分布方程的热不稳定性，并给出此类问题的热不稳定性的判据。     

The theory of relativity and super-luminal-speeds

According to some local properties of Lorentz transformation, Einstein stated: Velocities greater than that of light have no possibility of existence. He neglected to point out the applicable range of the special theory of relativity. In fact, it could only be applied to the subluminal-speed. This paper shows that if we think of the possibility of the existence of the superluminal-speed and redescribe the special theory of relativity following Einstein's way, a new kinematic theory would be founded. The new theory would retain all kinematical meaning of the special theory of relativity when matters move with subluminal-speed and would give new content when matters move with superluminal-speed. The paper also discusses the observation principle for the motions with superluminal-speed.     

Physical uniformity of the Universe

The question of the spatial homogeneity of the Universe is re-examined from the viewpoint of the hypothesis on the physical unity of the universe. It is shown that the demand for the universal validity of the theory of relativity implies that the average value of the Newtonian world potential is constant everywhere in the universe which is spatially homogeneous on a large scale. It turns out that Mach's principle is compatible with the special theory of relativity if the average value of the normalized world potential is exactly equal to–c ². This fact may be interpreted as a consequence of the fundamental idea of the general relativity that cosmic matter determines the space-time metric in agreement with Mach's principle.     

Gravitationless black holes

A gravitationless black hole model is proposed in accord with a five-dimensional fully covariant Kaluza-Klein (K-K) theory with a scalar field, which unifies the four-dimensional Einsteinian general theory of relativity and Maxwellian electromagnetic theory. It is shown that a dense compact core of a star, when it collapses to a critical density, suddenly turns off or shields its gravitational field. The core, if its mass exceeds an upper limit, directly collapses into a black hole. Otherwise, the extremely large pressure, as the gravity is turned off, immediately stops the collapse and drives the mantle material of supernova moving outward, which leads to an impulsive explosion and forms a neutron star as a remnant. A neutron star can further evolve into a black hole when it accretes enough matter from a companion star such that the total mass exceeds a lower limit. The black hole in the K-K theory is gravitationless at the surface because the scalar field is infinitely strong, which varies the equivalent gravitational constant to zero. In general, a star, at the end of its evolution, is relatively harder to collapse into a gravitationless K-K black hole than a strong gravitational Schwarzschild black hole. This is consistent with the observation of some very massive stars to form neutron stars rather than expected black holes. In addition, the gravitationless K-K black hole should be easier to generate jets than a Schwarzschild black hole.     

Number of information and its relation to the cosmological constant resulting from Landauer’s principle

In this study, we have investigated the geometrical and physical properties of stationary axisymmetric solutions. The expressions for the axial-vector and the gravitational energy and momentum densities are obtained in the context of teleparallel equivalent of general relativity. The obtained results are compared with that obtained previously in the context of Møller’s tetrad theory of gravitation. We discussed special cases of these solutions.     

The possible compatibility of Einstein's general theory of relativity,Mach's principle,and Rosen's bimetric theory,in relation to Horák's cosmic potential

Mach's principle is formulated in two different ways, heuristic and mathematical. Known problems of the principle are listed and two of them, the problem of its validity in the case the Universe is open and the boundary condition problem, are analyzed separately. Moreover, the history of the cosmic potential is outlined and a short modification of Horák's deduction of the potential is presented together with a discussion on the conditions of the solution. The conclusions are drawn that the Universe is closed and that Mach's principle is compatible with the general theory of relativity, provided that the Big Bang did not start from a singularity but from finite volume and density. In the last section it is shown that Rosen's bimetric theory is compatible with our picture of the Universe.     

Exact Bianchi Type-I Cosmological Micro Model in Modified Theory of General Relativity

An anisotropic, homogeneous Bianchi type-I cosmological micro model is obtained in Barber's modified theory of general relativity. Some properties of the model are discussed. Further, it is found that this theory leads to Einstein theory as the coupling parameterλ → 0 in micro level (i.e., quantum level) in general. This revised version was published online in July 2006 with corrections to the Cover Date.     

Energy of a Stringy Charged Black Hole in the Teleparallel Gravity

We use the teleparallel geometry analog of the Møller energy-momentum complex to calculate the energy distribution (due to matter plus field including gravity) of a charged black hole solution in heterotic string theory. We find the same energy distribution as obtained by Gad who investigated the same problem by using the Møller energy-momentum complex in general relativity. The total energy depends on the black hole mass M and charge Q. The energy obtained is also independent of the teleparallel dimensionless coupling constant, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model. Furthermore, our results also sustains (a) the importance of the energy-momentum definitions in the evaluation of the energy distribution of a given spacetime and (b) the viewpoint of Lessner that the Møller energy-momentum complex is a powerful concept of energy and momentum.     

Computer applications to lunar and artificial satellite laser ranging

The University of Texas McDonald Observatory has long been a pioneer in acquiring laser ranging data, a data type which has substantially improved our knowledge of the dynamics of the earth-moon system as well as various aspects of geophysics and general relativity. (See Mulholland, 1980; Shelus, 1985; Shelus, 1987.) The McDonald Laser Ranging System (MLRS) is one of only 2 laser ranging stations world-wide having the capability of routine data acquisition on both lunar and artificial satellite targets (Shelus,IEEE, 1985). In this paper we discuss the current applications of modern computer technology to the problems of acquiring and reducing that ranging data. As technology continues to improve, the logical upgrade is the replacement of obsolescent station minicomputers with the resource-rich environment of micro-computers. The goal is to allow the automation of many station ranging functions as well as the enhancement of onsite data quality control, filtering, and analysis. Plans for such upgrades and their implications for dynamical astronomy are discussed.     

Equations of radiation gas dynamics in tetrad form for astrophysical applications

This paper deals with the representation of relativistic equations of gas dynamics with due regard to the general relativity theory effects in the form accepted and widely applied in the special relativity theory. With this purpose, a strict formal definition of a non-inertial co-moving reference frame without rotation is carried out on the basis of a tetrad formalism by use of the Fermi—Walker rules of transport of 4-frame. The equations of physical kinetics, relativistic collapse, Einstein's equations, equations of relatiivistic radiation gas dynamics for ideal and dissipative gases, Taub's equations for a shock wave, which allow for radiation and electron-positron pairs, are obtained in this reference frame. On the basis of the local Lorentz transformation and the Ricci rotation coefficients, these equations are written in the laboratory reference frame, in order to illustrate the fact that the general relativity effects can be simply taken into account in the equations having a form accepted in the special relativity theory.