Moshe Carmeli

Cosmological relativity: a new theory of cosmology

A new general-relativistic theory of cosmology, the dynamical variables of whichare those of Hubbles, namely distances and redshifts, is presented. The theorydescribes the universe as having a three-phase evolution with a deceleratingexpansion followed by a constant and an accelerating expansion, and it predictsthat the universe is now in the latter phase. The theory is actually a generalizationof Hubbles law taking gravity into account by means of Einsteins theory ofgeneral relativity. The equations obtained for the universe expansion are elegantand very simple. It is shown, assuming Ω0 = 0.24, that the time at which theuniverse goes over from a decelerating to an accelerating expansion, i.e., theconstant expansion phase, occurs at 0.03 τ from the big bang, where τ is theHubble time in vacuum. Also, at that time the cosmic radiation temperature was11 K. Recent observations of distant supernovae imply, in defiance of expectations,that the universes growth is accelerating, contrary to what has always beenassumed, that the expansion is slowing down due to gravity. Our theory confirmsthese recent experimental results by showing that the universe now is definitelyin a stage of accelerating expansion.

Reformulation of general relativity as a gauge theory

Abstract The starting point is a spinor affine space-time. At each point, two-component spinors and a basis in spinor space, called “spin frame,” are introduced. Spinor affine connections are assumed to exist, but their values need not be known. A metric tensor is not introduced. Global and local gauge transformations of spin frames are defined with GL(2) as the gauge group. Gauge potentials Bμ are introduced and corresponding fields Fμν are defined in analogy with the Yang-Mills case. Gravitational field equations are derived from an action principle. Incases of physical interest SL(2, C) is taken as the gauge group, instead of GL(2). In the special case of metric space-times the theory is identical with general relativity in the Newman-Penrose formalism. Linear combinations of Bμ are generalized spin coefficients, and linear combinations of Fμν are generalized Weyl and Ricci tensors and Ricci scalar. The present approach is compared with other formulations of gravitation as a gauge field.

Field theory onR×S3 topology. I: The Klein-Gordon and Schrödinger equations

A Klein-Gordon-type equation onR×S3 topology is derived, and its nonrelativistic Schrödinger equation is given. The equation is obtained with a Laplacian defined onS3 topology instead of the ordinary Laplacian. A discussion of the solutions and the physical interpretation of the equation are subsequently given, and the most general solution to the equation is presented.

Field theory onR× S 3 topology. III: The Dirac equation

A Dirac-type equation on R×S3 topology is derived. It is a generalization of the previously obtained Klein-Gordon-type, Schrödinger-type, and Weyl-type equations, and reduces to the latter in the appropriate limit. The (discrete) energy spectrum is found and the corresponding complete set of solutions is given as expansions in terms of the matrix elements of the irreducible representations of the group SU2. Finally, the properties of the solutions are discussed.

Cosmological special relativity : the large-scale structure of space, time and velocity

Cosmological special relativity: fundamentals of special relativity present-day cosmology postulates cosmic frames space velocity in cosmology pre-special-relativty relative cosmic time inadequacy of classical transformation universe expansion versus light derivation of the transformation interpretation of the transformation another derivation consequencs of the transformation. Extension of the Lorentz Group to cosmology: the line element the transformations explicity the most general transformation. Fundamentals of special relativity: postulates of special relativity the Galilean transformation the Lorentz transformation consequences of the Lorentz transformation four-dimensional structure of spacetime the light cone mass, energy and momentum.

Field theory onR× S 3 topology. II: The Weyl equation

A Weyl-type equation onR×S3 topology is derived, as a generalization to previously obtained Klein-Gordon- and Schrödinger-type equations for the same topology. The general solution of the new equation is given as an expansion in the matrix elements of the irreducible representations of the groupSU2. The properties of the solutions are discussed.

Gravitational Field of a Radiating Rotating Body

Abstract A nonstationary solution of the Einstein field equations, corresponding to the field of a radiating rotating body, is presented. The solution is algebraically special of Petrov type II with a twisting, shear-free, null congruence identical to that of the Kerr metric. The new metric bears the same relation to the Kerr metric as does Vaidyas metric to the Schwarzschild metric, in the sense that in both cases the radiating solution is generated from the nonradiating one by replacing the mass parameter by an arbitrary function of a retarded time coordinate. The energy-momentum tensor in the present case, however, has two terms, a Vaidya type radiative one and an additional nonradiative residual term. Due to the presence of the nonradiative term in this case, however, the energy-momentum tensor becomes Vaidya-like asymptotically only, thus allowing for a geometrical optics interpretation. Asymptotically, part of the radiation field is purely electromagnetic with a Maxwell tensor which admits only one principal null direction corresponding to the undirectional flow of radiation.

Group‐Theoretic Approach to the New Conserved Quantities in General Relativity

The Newman‐Penrose formalism for obtaining the recent conserved quantities in general relativity is discussed and a group‐theoretic interpretation is given to it. This is done by relating each triad of the orthonormal vectors on the sphere to an orthogonal matrix g. As a result, the spin‐weighted quantities η become functions on the group of three‐dimensional rotation, η = η(g), where g ∈ O3. An explicit form for the matrix g is given and a prescription for rewriting η(g) as functions of the spherical coordinates is also given. We show that a quantity of spin weight s can be expanded as a series in the matrix elements Tsmj of the irreducible representation of O3, where s is fixed. Infinite‐ and finite‐dimensional representations of the group SU2 are then realized in the spaces of ηs and Tsmj. It is shown that the infinite‐dimensional representation is not irreducible; its decomposition into irreducible parts leads to the expansion of η in the Tsmj, the latter providing invariant subspaces in which irredu...

Value of the Cosmological Constant in the Cosmological Relativity Theory

It is shown that the cosmological relativity theory predicts the value Λ = 1.934 × 10−35s−2 for the cosmological constant. This value of Λ is in excellent agreement with the measurements recently obtained by the High-Z Supernova Team and the Supernova Cosmology Project.

Group theory and general relativity : representations of the Lorentz group and their applications to the gravitational field

The rotation group the Lorentz group spinor representation of the Lorentz group principal series of representations of SL(2,C) complementary series of representations of SL(2,C) complete series of representations of SL(2,C) elements of general relativity theory spinors in general relativity SL(2,C) gauge theory of the gravitational field - the Newman-Penrose equations analysis of the gravitational field some exact solutions of the gravitational field equations the Bondi-Metzner-Sachs Group.