Gravi-inertial reference frames in Schwarzschild and Kerr spaces

Gravi-inertial reference frames — the analogue of inertial frames in two-dimensional space — are constructed in Schwarzschild and Kerr spaces. With their help the energy, momentum, and angular momentum of these systems are determined. A form is found for writing Kerr's solution in Bondi-Sachs coordinates in the slow-rotation approximation. A new solution of Einstein's equations is found in this approximation which describes the gravitational field of a rotating and radiating source.     

Determination of the Lagrangian of the tetrad gravitational field

By requiring correspondence with Newtonian gravitational theory and the Lorentz covariant theory of nongravitational matter and by establishing the simplest possible form of the linear approximation of the field equations, the gravitational Lagrangian of the tetrad theory of gravitation is determined uniquely. It contains two characteristic constants: Einstein's gravitational constant and the specific dimensionless “teleparallel” constant ω ≈ 1.     

On gravitational shock waves in curved spacetimes

Some years ago Dray and 't Hooft found the necessary and sufficient conditions to introduce a gravitational shock wave in a particular class of vacuum solutions to Einstein's equations. We extend this work to cover cases where non-vanishing matter fields and a cosmological constant are present. The sources of gravitational waves are massless particles moving along a null surface such as a horizon in the case of black holes. After we discuss the general case we give many explicit examples. Among them are the d-dimensional charged black hole (that includes the 4-dimensional Reissner-Nordström and the d-dimensional Schwarzschild solution as subcases), the 4-dimensional De Sitter and anti-De Sitter spaces (and the Schwarzschild-De Sitter black hole), the 3-dimensional anti-De Sitter black hole, as well as backgrounds with a covariantly constant null Killing vector. We also address the analogous problem for string-inspired gravitational solutions nd give a few examples.     

Electromagnetic and Force Field Equations

In classical physics the electromagnetic equations are described by Maxwell's equations. Maxwell's equations proved to be invariant under gauge, or Lorentz transformations. Also, Einstein's equations of the special theory of relativity are invariant under Lorentz transformations. On the other hand classical mechanics and quantum mechanics laws are invariant under Galilean transformations. This means that, there are two different dynamical structures describing our universe. Einstein's unified field theory failled in putting our universe in one dynamical structure. New electromagnetic and force field equations are going to be derived. They have the same shape like Maxwell's equations, but with different dynamical structure. Those equations are invariant under Galilean transformations and in the density matrix formalism of quantum mechanics.     

Extended Einstein–Cartan theory à la Diakonov: The field equations

Diakonov formulated a model of a primordial Dirac spinor field interacting gravitationally within the geometric framework of the Poincaré gauge theory (PGT). Thus, the gravitational field variables are the orthonormal coframe (tetrad) and the Lorentz connection. A simple gravitational gauge Lagrangian is the Einstein–Cartan choice proportional to the curvature scalar plus a cosmological term. In Diakonov?s model the coframe is eliminated by expressing it in terms of the primordial spinor. We derive the corresponding field equations for the first time. We extend the Diakonov model by additionally eliminating the Lorentz connection, but keeping local Lorentz covariance intact. Then, if we drop the Einstein–Cartan term in the Lagrangian, a nonlinear Heisenberg type spinor equation is recovered in the lowest approximation.     

Theory of Gravitational-Inertial Field of Universe

In this paper the basic proposition is a generalization of the metric tensor by introduction of an inertial field tensor satisfying ?_ig_lm ? g_lm;i ≠ 0. On the basis of variational equations a system of more general covariant equations of gravitational-inertial field is obtained. In Einstein's approximation these equations reduce to the field equations of Einstein. The solution of fundamental problems of generl taheory of relativity by means of the new equations give the same results as Einstein's equations. However application of these equations to the cosmologic problem leads to following results: 1. All Galaxies in the Universe (actually all bodies if gravitational attraction is not considered) “disperse” from each other according to Hubble's law. Thus contrary to Friedmann's theory (according to which the “expansion of Universe” began from the singular state with an infinite velocity) the velocity of “dispersion” of bodies begins from the zero value and in the limit tends to the velocity of light. 2. The “dispertion” of bodies represents a free motion in the inertial field and Hubble's law represents a law of motion of free bodies in the inertial field - the law of inertia. All critical systems (with Schwarzschild radius) are specific because they exist in maximal inertial and gravitational potentials. The Universe represents a critical system, it exists under the Schwarzschild radius. In the high-potential inertial and gravitational fields the material mass in a static state or in the process of motion with decelleration is subject to an inertial and gravitational “annihilation”. Under the maximal value of inertial and gravitational potentials (= c²) the material mass is completely “evaporated” transforming into a radiation mass. The latter is concentrated in the “horizon” of the critical system. All critical systems –“black holes”- represent geon systems, i.e., the local formations of gravitational-electromagnetic radiations, held together by their own gravitational and inertial fields. The Universe, being a critical system, is “wrapped” in a geon crown. The Universe is in a state of dynamical equilibrium. Near the external part of its boundary surface a transformation of matter into electromagnetic-gravitational-neutrineal energy (geon mass) takes place. Inside the Universe, in the galaxies takes place the synthesis of matter from geon mass, penetrating from the external part of the world (from geon crown) by means of a tunneling mechanism. The geon system may be considered as a natural entire cybernetic system.     

Can quantum gravitational forces stop gravitational collapse?

We consider, in lowest order of the gravitational coupling constant G, the gravitational potential between two neutrons. As we have previously pointed out [1],the quantum (including spin) contributions to the gravitational field dominate for distances smaller than the Compton wavelength of the neutron. At such distances the gravitational force between two neutrons may be repulsive. In particular, the gravitational forces which are analogous to the familiar Darwin and Fermi forces of quantum electrodynamics are capable of stopping gravitational collapse. Our discussion is within the framework of Einstein's theory, but on a microscopic level. We conclude that gravitational collapse may be halted without the necessity of extending Einstein's theory à la Cartan or otherwise.     

Über mögliche Grenzen einer Gravitationstheorie

On Possible Limits of a Gravitation Theory This work intends to answer the question why gravitational phenomena are described just by a theory which make use of a Riemannian metric tensor that has to be a solution of the known Einstein equations. The answer is thought of as a link from Maupertuis's principle to Einstein's equations, which appear as a transformed integrability condition. The metric tensor is first formally introduced and direction dependent (a Finslerian one) and then reduced to a Riemannian one by means of the condition of local Lorentz invariance. The construction seems to show that the gravity concept could not have a sense at the atomic level as a consequence of the central role which plays the particle-motion in the whole.     

The Sugawara model in general relativity. A. The case for three current vectors (SU (2))

A general method of solving the equations of Sugawara's field theory of currents has been developed, and illustrated by applying it to the set of three currents. These are inserted into Einstein's field equations which have been solved together with the co-variant ‘gauge’ conditions for a gravitational field involving cylindrical symmetry. A further transformation exhibits the triad formed by the current vectors and exhibits clearly the deviations of the line-element from Schwarzschild's exterior solution. In a subsequent paper the case for eight vector currents corresponding toSU (3) will be treated in similar fashion.     

A general integral of the Jordan-Brans-Dicke field equations for static spherically symmetric perfect fluid distributions

The Jordan-Brans-Dicke field equations [1] contain the four-dimensional field equations of the five-dimensional projective unified theory. As it should be, Einstein's theory is incorporated as a limiting case. In this paper we present a method to determine explicitly for every static spherically symmetric solution of Einstein's theory with perfect fluid an analogous solution of Jordan-Brans-Dicke theory. As a particular example a “generalized interior Schwarzschild solution” is given.     

Numerical Relativity and the Discovery of Gravitational Waves

Solving Einstein's equations precisely for strong‐field gravitational systems is essential to determining the full physics content of gravitational wave detections. Without these solutions it is not possible to infer precise values for initial and final‐state system parameters. Obtaining these solutions requires extensive numerical simulations, as Einstein's equations governing these systems are much too difficult to solve analytically. These difficulties arise principally from the curved, non‐linear nature of spacetime in general relativity. Developing the numerical capabilities needed to produce reliable, efficient calculations has required a Herculean 50‐year effort involving hundreds of researchers using sophisticated physical insight, algorithm development, computational technique, and computers that are a billion times more capable than they were in 1964 when computations were first attempted. The purpose of this review is to give an accessible overview for non‐experts of the major developments that have made such dramatic progress possible.     

The significance of curvature in general relativity

In General Relativity, one has several traditional ways of interpreting the curvature of spacetime, expressed either through the curvature tensor or the sectional curvature function. This essay asks what happens if curvature is treated on a more primitive level, that is, if the curvature is prescribed, what information does one have about the metric and associated connection of space-time? It turns out that a surprising amount of information is available, not only about the metric and connection, but also, through Einstein's equations, about the algebraic structure of the energy-momentum tensor.     

Gravitation and Riemannian space

The field equations of the quadratic action principle of relativity are solved, assuming a weak perturbation of the basic structure, which is a highly agitated Riemannian lattice field of a very small lattice constant. A field emerges which can be interpreted as the weak gravitational field of an apparently Minkowskian space. This field does not coincide with Einstein's theory of weak gravitational fields. Whereas the redshift remains unchanged, the light deflection becomes reduced by11.1% of the value predicted by Einstein.     

Cosmology and Description of Local Space-Time Properties by Einstein's Equations

We consider a theory in which the global and local space-time properties are described by different laws. One consequence of such a theory is that the only time-dependent cosmological models are such that their homogeneous and isotropic three-spaces are closed. In the framework of this theory the local space-time properties are approximately described bei Einstein's equations, but with Einstein's gravitational coupling number now being a function of the matter density filling the universe.     

Planck's Orders of Magnitude and the Limits of the Quantum Gravity Conception

Considering gravitational Euler scattering and energy fluctuations of gravitational Planck radiation it is shown that - due to the nonlinearity of Einstein's equations - there arise effective cut-of lengths preventing the measurability of quantum vacuum effects near Planck's length.     

Electro-geometrodynamics

By distinguishing between the metric of a Riemannian geometry and the interval defining function it is demonstrated that both Einstein's gravitational field equations and Maxwell's electromagnetic field equations can be generated from a single geometry.     

Curvature collineations and the determination of the metric from the curvature in general relativity

It is shown that for a very general class of space-times, the componentsR _bcd ^a of the curvature tensor determine the metric components up to a constant conformal factor. This general class contains most of those cases which are usually considered to be interesting from the point of view of Einstein's general relativity theory. The connection between the above result and the existence of proper curvature collineations is given.