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We investigate the question of how an observer in 4D perceives the five-dimensional geodesic motion. We consider the interpretation of null and non-null bulk geodesics in the context of brane theory, space-time-matter theory (STM) and other non-compact approaches. We develop a "frame-invariant" formalism that allows the computation of the rest mass and its variation as observed in 4D. We find the appropriate expression for the four-acceleration and thus obtain the extra force observed in 4D. Our formulae extend and generalize all previous results in the literature. An important result here is that the extra force in brane-world models with Z2-symmetry is continuous and well defined across the brane. This is because the momentum component along the extra dimension is discontinuous across the brane, which effectively compensates the discontinuity of the extrinsic curvature. We show that brane theory and STM produce identical interpretation of the bulk geodesic motion. This holds for null and non-null bulk geodesics. Thus, experiments with test particles are unable to distinguish whether our universe is described by the brane world scenario or by STM. However, they do discriminate between the brane/STM scenario and other non-compact approaches. Among them the canonical and embedding approaches, which we examine in detail here. [ABSTRACT FROM AUTHOR]

The problem of constructing a model of an extended charged particle within the context of general relativity has a long and distinguished history. The distinctive feature of these models is that, in some way or another, they require the presence of negative mass in order to maintain stability against Coulomb's repulsion. Typically, the particle contains a core of negative mass surrounded by a positive-mass outer layer, which emerges from the Reissner-Nordström field. In this work we show how the Einstein-Maxwell field equations can be used to construct an extended model where the mass is positive everywhere. This requires the principal pressures to be unequal inside the panicle. The model is obtained by setting the "effective" matter density, rather than the rest matter density, equal to zero. The Schwarzschild mass of the panicle arises from the electrical and gravitational field (Weyl tensor) energy. The model satisfies the energy conditions of Hawking and Ellis. A particular solution that illustrates the results is presented. [ABSTRACT FROM AUTHOR]

A new class of spherically symmetric solutions of the Einstein field equations is presented. Their main features are that (i) the azimuthal metric coefficient depends on time only, and (ii) they possess similarity symmetry. The physical motivation for the study of such class of solutions is that according to recent investigations [R. N. Henriksen, A. G. Emslie, and P. S. Wesson, Phys. Rev. D 27, 1219 (1983); P. S. Wesson, Phys. Rev. D 34, 3925 (1986)], they can be relevant to ‘‘bubbles’’ of new phases, in phase transitions typical of inflationary universe models. The solutions have shear, are inhomogeneous, and may be interpreted as ‘‘mixtures’’ of perfect fluids. They have some adjustable parameters which can be used to assure the fulfillment of the energy conditions. There are two different types of solutions. One of them has similarity symmetry of the first kind and negative total pressure. These models can be used in a classical description of particle production phases in the early universe. The other type of solution has similarity of the second kind, i.e., it represents models with dimensional constraints. Explicit solutions representing mixtures of fluids with equations of state p=nρ and ρ=p of this type are given. They may be useful for cosmological models in closed universes. The dimensional constraints are found to be due to the ‘‘boundary conditions’’ in such universes. The specific characteristics of both types of solutions suggest that a transition from a particle-production phase to a radiation-dominated era can be described by means of bubbles of a ‘‘broken-symmetry’’ phase with positive pressure growing into a region of ‘‘unbroken-symmetry’’ phase with negative pressure. [ABSTRACT FROM AUTHOR]

A number of aspects of the phenomenon of gravitational repulsion in static sources of the Reissner–Nordström field are investigated. It is found that in the case of perfect fluid spheres there exists a close relation between this phenomenon and the Weyl curvature tensor. In fact, it is proved that such a source gives rise to gravitational repulsion only if the pure gravitational field energy inside the sphere is negative. It is also proved that although the gravitational repulsion always takes place in the interior of a perfect fluid charged sphere when its radius r0 is less than the ‘‘classical electron radius’’ re, this is not necessarily so either in the case of anisotropic charged spheres or if the net charge of the body is concentrated at its boundary only. It is shown that the phenomenon can also occur inside charged sources with r0>re. New sources of repulsive gravitation are constructed. They differ from others in the literature, since they neither satisfy the equation of state of ‘‘false vacuum’’ nor are their total gravitational masses entirely of electromagnetic origin. It is found that the charge contributes negatively to the effective gravitational mass MG, in the sense that an increase in the charge causes a decrease in MG. The gravitational repulsion in the new models constructed here is explained as due to this negative contribution rather than due to the strain of vacuum because of vacuum polarization. [ABSTRACT FROM AUTHOR]