The general relativity with conformal units

General Relativity rewritten in conformal units identifies conformal intervals with the real observational distances. This identification gives a base to explain all epochs of the Universe evolution including Ia supernova luminosity long distance-redshift relation by the dominance of the Casimir vacuum energy of all physical fields. A set of arguments is discussed in favor that SNe Ia data in the conformal units can be an evidence of the conformal twistor structure of the space-time as a nonlinear realization of the affine group, like the nonlinear realization of chiral symmetry and phenomenological Lagrangian is evidence of the quark structure of hadrons.     

Energy and momentum in general relativity

In general relativity, conservation of energy and momentum is expressed by an equation of the form /x= 0, where –gT represents the total energy, momentum, and stress. This equation arises from the divergence formula dV _v = (/x ^v )d ⁴ d. Here we show that this formula fails to account properly for the system of basis vectors e(x). We obtain the (invariant) divergence formula e dV _v = e (/x ^v + )d ⁴ d. Conservation of energy and momentum is therefore expressed by the covariant equation (/x ^v ) + = 0. We go on to calculate the variation of the action under uniform displacements in space-time. This calculation yields the covariant equation of conservation, as well as the fully symmetric energy tensor . Finally, we discuss the transfer of energy and momentum, within the context of Einstein's theory of gravitation.     

Special conformal symmetries in general relativity

A geometrical discussion of special conformal vector fields in space-time is given. In particular, it is shown that if such a vector field is admitted, it is unique up to a constant scaling and the addition of a homothetic or a Killing vector field. In the case when the gradient of the conformal scalar associated with is non-null it is shown that other homothetic and affine symmetries are necessarily admitted by the space-time, that an intrinsic family of 2-dimensional flat submanifolds is determined in the space-time, that is, in general, hypersurface orthogonal and that the space-time, if non-flat, is necessarily (geodesically) incomplete. Other geometrical features of such space-times are also considered.     

Integral constraints in general relativity

Using a covariant formalism we derive the conditions for there to exist integral constraints on energy-momentum perturbations in an arbitrary background spacetime.     

The energy and the linear momentum of space-times in general relativity

We extend our previous proof of the positive mass conjecture to allow a more general asymptotic condition proposed by York. Hence we are able to prove that for an isolated physical system, the energy momentum four vector is a future timelike vector unless the system is trivial. Furthermore, we allow singularities of the type of black holes.Supported in part by an NSF grant     

Angular momentum of isolated systems in general relativity

Solutions of Einstein's equations which describe isolated scattering systems are discussed and a set of asymptotic boundary conditions, which appear to characterize such solutions, is proposed. These conditions are then used to obtain a canonical definition of the total amount of angular momentum radiated by such a system.S.R.C. postdoctoral research fellow.     

Five-dimensional teleparallel theory equivalent to general relativity, the axially symmetric solution, energy and spatial momentum

A theory of (4+1)-dimensional gravity is developed on the basis of the teleparallel theory equivalent to general relativity. The fundamental gravitational field variables are the five-dimensional vector fields (pentad), defined globally on a manifold M, and gravity is attributed to the torsion. The Lagrangian density is quadratic in the torsion tensor. We then give the exact five-dimensional solution. The solution is a generalization of the familiar Schwarzschild and Kerr solutions of the four-dimensional teleparallel equivalent of general relativity. We also use the definition of the gravitational energy to calculate the energy and the spatial momentum.     

The gravitational contribution to the momentum of a medium in general relativity

The time-space components of the macroscopic stress-energy tensor of a medium in general relativity (derived in a previous paper) are examined for the momentum density and energy flux of the microscopic gravitational fields. Agreement with both the Newtonian approximation and Chandrasekhar's post-Newtoninan approximation is noted.     

Angular momentum,magnetic moment,andg-factor in general relativity

The solutions to the Einstein-Maxwell equations for the case of a slowly rotating, massive thin shell with arbitrary charge are investigated. The form of the metric chosen here facilitates a more detailed analysis of the shell's angular momentum, magnetic moment, andg-factor than in earlier work. In addition to confirming earlier results, it is found that, for a charge-to-mass ratio greater than unity there is no upper or lower bound on the valueg may take and that the magnetic moment and net angular momentum of the shell may vanish or change sign (relative to the sense of rotation).     

Symmetry constraints in general relativity and the Schwarzchild interior metric

Einstein's equations with a perfect fluid source are subjected to compatibility conditions in the context of a space-time that contains symmetric subspaces. These conditions constitute, in some cases, a powerful tool for exhibiting the solutions to a given problem. The Schwarzchild interior metric in conformally flat coordinates is derived using these methods.     

Solutions of five-dimensional general relativity without spatial symmetry

Conformastationary solutions of the five-dimensional vacuum Einstein equations, depending on one or two harmonic potentials, are constructed. The solutions depending on one potential fall in three distinct classes. Solutions of two of these classes may be combined to yield a class of solutions depending on two potentials, which correspond to the Israel-Wilson-Perjès solutions of the Einstein-Maxwell theory. The asymptotically flat solutions of this class describe systems of rotating electric or magnetic monopoles.     

Cauchy problems for the conformal vacuum field equations in general relativity

Cauchy problems for Einstein's conformal vacuum field equations are reduced to Cauchy problems for first order quasilinear symmetric hyperbolic systems. The “hyperboloidal initial value” problem, where Cauchy data are given on a spacelike hypersurface which intersects past null infinity at a spacelike two-surface, is discussed and translated into the conformally related picture. It is shown that for conformal hyperboloidal initial data of classH ^S,s≧4, there is a unique (up to questions of extensibility) development which is a solution of the conformal vacuum field equations of classH ^S. It provides a solution of Einstein's vacuum field equations which has a smooth structure at past null infinity.     

The momentum conservation law in special relativity

The derivation of the functional form of the relativistic momentum of a particle has a history going back to Lewis and Tolman's paper of 1909, yet satisfactory presentations seem to be few in number. Careful examination of the several types of derivation shows that their shortcomings are avoidable and allows the presentation of exact and improved analyses.     

Energy, momentum and angular momentum in the dyadosphere of a charged spacetime in teleparallel equivalent of general relativity

We apply the energy momentum and angular momentum tensor to a tetrad field,with two unknown functions of radial coordinate,in the framework of a teleparallel equivalent of general relativity(TEGR).The definition of the gravitational energy is used to investigate the energy within the external event horizon of the dyadosphere region for the Reissner-Nordstrm black hole.We also calculate the spatial momentum and angular momentum.     

Energy, momentum and angular momentum in the dyadosphere of a charged spacetime in teleparallel equivalent of general relativity

We apply the energy momentum and angular momentum tensor to a tetrad field, with two unknown functions of radial coordinate, in the framework of a teleparallel equivalent of general relativity (TEGR). The definition of the gravitational energy is used to investigate the energy within the external event horizon of the dyadosphere region for the Reissner-Nordström black hole. We also calculate the spatial momentum and angular momentum.     

Simplification of the constraints in the dirac formalism for general relativity

In any classical theory in canonical form, the Poisson bracket relations between the constraints are preserved under canonical transformations. We show that in the Dirac formalism for general relativity this condition places certain limits on the degree to which one can simplify the form of the constraints. It implies, for instance, that the constraints cannot all be written as canonical momenta. Furthermore, it is not even possible to reduce them all to purely algebraic functions of the momenta by means of a canonical tansformation which preserves the original configuration space subspace of phase space.     

Simplification of the constraints in the dirac formalism for general relativity

In any classical theory in canonical form, the Poisson bracket relations between the constraints are preserved under canonical transformations. We show that in the Dirac formalism for general relativity this condition places certain limits on the degree to which one can simplify the form of the constraints. It implies, for instance, that the constraints cannot all be written as canonical momenta. Furthermore, it is not even possible to reduce them all to purely algebraic functions of the momenta by means of a canonical tansformation which preserves the original configuration space subspace of phase space.