卷 24, 编号 1 (2018)

Solutions describing regular rotating black holes are typically obtained by applying the Newman-Janis complex translation to spherical metrics of the Kerr-Schild class. Regular solutions of this class are specified by T_t^t = T_r^r and have necessarily de Sitter centers provided that the source terms T_kⁱ satisfy the weak energy condition. Rotation transforms a de Sitter center into a de Sitter vacuum disk which is the generic common constituent of all regular rotating objects. In nonlinear electrodynamics coupled to gravity all metrics belong to the Kerr-Schild class and have the Kerr-Newman asymptotic for a distant observer. The ring singularity is replaced with the superconducting ring current which represents an electromagnetic nondissipative source of any asymptotically Kerr-Newman geometry. We outline the basic generic features of regular rotating black holes and solitons which are regular compact objects without event horizons, replacing naked singularities.

Cosmological dynamics is studied in Einstein–Gauss–Bonnet gravity with a perfect fluid source in arbitrary dimension. A systematic analysis is performed for the case that the theory does not admit maximally symmetric solutions. Considering two independent scale factors, namely, one for the 3D space and one for the extra-dimensional space, it is found that a regime exists where the scale factor of extra dimensions tends to a constant value via damped oscillations for not too negative pressure of the fluid, so that asymptotically the evolution of the (3 + 1)-dimensional Friedmann model with perfect fluid is recovered.

In the author’s previous publications, a recursive linear algebraic method was introduced for obtaining (without gravitational radiation) the full potential expansions for the gravitational metric field components and the Lagrangian for a general N-body system. Two apparent properties of gravity— Exterior Effacement and Interior Effacement—were defined and fully enforced to obtain the recursive algebra, especially for the motion-independent potential expansions of the general N-body situation. The linear algebraic equations of this method determine the potential coefficients at any order n of the expansions in terms of the lower-order coefficients. Then, enforcing Exterior and Interior Effacement on a selecedt few potential series of the full motion-independent potential expansions, the complete exterior metric field for a single, spherically-symmetric mass source was obtained, producing the Schwarzschild metric field of general relativity. In this fourth paper of this series, the complete spatial metric’s motion-independent potentials for N bodies are obtained using enforcement of Interior Effacement and knowledge of the Schwarzschild potentials. From the full spatial metric, the complete set of temporal metric potentials and Lagrangian potentials in the motion-independent case can then be found by transfer equations among the coefficients κ(n, α) → λ(n, ε) → ξ(n, α) with κ(n, α), λ(n, ε), ξ(n, α) being the numerical coefficients in the spatial metric, the Lagrangian, and the temporal metric potential expansions, respectively.

We first motivate the study of viscosity in cosmology. Whilst most studies assume that the universe is filled with a perfect fluid, viscosity is expected to play a role, at least during some stages of the evolution of the Universe. There are several theories of viscosity. Eckart’s first-order theory was found to permit superluminal signals, and equilibrium states were found to be unstable. To solve these problems, the Israel-Stewart second-order theory was proposed. More recently, a relatively new first-order theory has appeared, which is claimed to also solve these problems.We briefly reviewthis first-order theory and present the basic field equations. Then we attempt to find homogeneous and isotropic solutions in the theory. It is noted that there do not exist stiff matter (pressure = energy density) solutions in the theory, in contrast to other theories. We then find power-law solutions without a cosmological term. Surprisingly, there do not exist simple exponential solutions, again in contrast to other theories. Finally, we present a solution with a cosmological term and make some concluding remarks.

We study the stability of different higher dimensional thin–shell wormholes (HDTSW) in general relativity with a cosmological constant. We show that a d-dimensional thin–shell wormhole surrounded by quintessence can have three different throat geometries: spherical, planar and hyperbolic. Unlike the spherical geometry, the planar and hyperbolic geometries allow different topologies that can be interpreted as higher-dimensional domain walls or branes connecting two universes. To construct these geometries, we use the cut-and-paste procedure by joining two identical vacuum space-time solutions. Properties such as the null energy condition and geodesics are also studied. A linear stability analysis around the static solutions is carried out, taking into account a more general HDTSW geometry than previous works, so it is possible to recover other well-known stability HDTSW conditions.

The problem of spinning and spin deviation equations for particles as defined by their microscopic effect has led many authors to revisit non-Riemannian geometry describing torsion and its relation with the spin of elementary particles. We obtain a new method for detecting the existence of torsion by deriving the equations of spin deviations in different classes of non-Riemannian geometries, using a modified Bazˆ anski method. We find that the translational and rotational gauge potentials regulate the spin deviation equation in the framework of the Poincare gauge field theory of gravity.

This paper forms part of an ongoing investigation to examine the quantum prediction that isolated baryons and electrons in the deep gravity wells of galaxy halos should exhibit reduced interaction cross-sections by virtue of the composition of the gravitational eigenspectra of their wave functions, and thereby identify a possible mechanism responsible for the origin of dark matter, without resorting to new physics or unknown particles. Relevant to this investigation are the electromagnetic state-to-state transition rates of charged particles occupying these gravitational eigenstates (EinsteinA coefficients), and, in the present work, we examine trends in these rates and net state lifetimes for particles in 1/r potential wells for values of the principal quantum number n and the angular momentum quantum number l. We find that transition rates decrease with increasing n and l, and that the rate is more steeply dependent on l when the quantum parameter Δp (≡ Δn − Δl) is greater, in agreement with earlier work. It is also found that there is an empirical relationship between the total state lifetime τ and the eigenvalues n and l, which is given by τ ∝ n^αl^β, where α ≈ 3 and β ≈ 2. The results apply equally to electrical potential wells, where the phenomena of reduced cross-sections and long radiative lifetimes is well known in the case of the Rydberg states of electrons in atoms. More importantly, in the case of gravitational eigenstates discussed here, the quantum prediction of low Einstein A (and therefore B) coefficients ofmany of the stateto-state transitions will mean that a particle whose eigenspectral composition consists of many of these weakly interacting states will be less likely to undergo scattering processes such as Compton scattering. Trends in the Einstein coefficients over the range of component eigenstates are required for calculating the net visibility and interaction rates of the generalized wave functions representing charged particles in macroscopic gravitational fields.