Cosmological Models with Time Dependent G and Λ Coupling Scalars

A cosmological model in which the universe has its critical density and gravitational constants generalized as coupling scalars in Einstein's theory is considered. A general method of solving the field equations is given. An exact solution for matter distribution in cosmological models satisfying G=G₀(R/R₀)ⁿ is presented. Corresponding physical interpretations of the cosmological solutions are also discussed.     

Conformally symmetric vacuum solutions of the gravitational field equations in the brane-world models

A class of exact solutions of the gravitational field equations in the vacuum on the brane are obtained by assuming the existence of a conformal Killing vector field, with non-static and non-central symmetry. In this case, the general solution of the field equations can be obtained in a parametric form in terms of the Bessel functions. The behavior of the basic physical parameters describing the non-local effects generated by the gravitational field of the bulk (dark radiation and dark pressure) is also considered in detail, and the equation of state satisfied at infinity by these quantities is derived. As a physical application of the obtained solutions we consider the behavior of the angular velocity of a test particle moving in a stable circular orbit. The tangential velocity of the particle is a monotonically increasing function of the radial distance and, in the limit of large values of the radial coordinate, tends to a constant value, which is independent on the parameters describing the model. Therefore, a brane geometry admitting a one-parameter group of conformal motions may provide an explanation for the dynamics of the neutral hydrogen clouds at large distances from the galactic center, which is usually explained by postulating the existence of the dark matter.     

Comment on `Five-Dimensional Cosmological Model with Variable

This comment corrects the small errors in the Letter of Baysal and Yilmaz [Chin. Phys. Lett. 24(2007)2185], where the case of n=1 was ignored. Meanwhile, the discussion in this comment on the case of n=-3 is novel, whichshows a potential reason why today the effect of the extra dimension has not been observed.     

Gauge Model Based on Group G×SU（2）

We present a model of gauge theory based on the symmetry group G×SU（2） where G is the gravitational gauge group and SU（2） is the internal group of symmetry. We employ the spacetime of four-dimensional Minkowski, endowed with spherical coordinates, and describe the gauge fields by gauge potentials. The corresponding strength field tensors are calculated and the field equations are written. A solution of these equations is obtained for the case that the gauge potentials have a particular form potentials induces a metric of Schwarzschild type on with spherical symmetry. The solution for the gravitational the gravitational gauge group space.     

A brief history of gravitational wave research

For the benefit of the readers of this journal, the editors requested that we prepare a brief review of the history of the development of the theory, the experimental attempts to detect them, and the recent direct observations of gravitational waves (GWs). The theoretical ideas and disputes beginning with Einstein in 1916 regarding the existence and nature of gravitational waves and the extent to which one can rely on the electromagnetic analogy, especially the controversies regarding the quadrupole formula and whether gravitational waves carry energy, are discussed. The theoretical conclusions eventually received strong observational support from the binary pulsar. This provided compelling, although indirect, evidence for gravitational waves carrying away energy—as predicted by the quadrupole formula. On the direct detection experimental side, Joseph Weber started more than fifty years ago. In 1966, his bar for GW detection reached a strain sensitivity of a few times ${10}^{?16}$. His announcement of coincident signals (now considered spurious), stimulated many experimental efforts from room temperature resonant masses to cryogenic detectors and laser-interferometers. Now there are km-sized interferometric detectors (LIGO Hanford, LIGO Livingston, Virgo and KAGRA). Advanced LIGO first reached a strain sensitivity of the order of ${10}^{?22}$. During their first 130 days of observation (O1 run), with the aid of templates generated by numerical relativity, they did make the first detections: two 5-σ GW events and one likely event. Besides earth-based GW detectors, the drag-free sensitivity of the LISA Pathfinder has already reached to the LISA goal level, paving the road for space GW detectors. Over the whole GW spectrum (from aHz to THz) there are efforts for detection, notably the very-low-frequency band (pulsar timing array [PTA], 300 pHz – 100 nHz) and the extremely-low (Hubble)-frequency (cosmic microwave background [CMB] experiment, 1 aHz – 10 fHz).     

New Taub–NUT–Reissner–Nordström spaces in higher dimensions

We construct new charged solutions of the Einstein–Maxwell field equations with cosmological constant. These solutions describe the nut-charged generalisation of the higher-dimensional Reissner–Nordström spacetimes. For a negative cosmological constant these solutions are the charged generalizations of the topological nut-charged black hole solutions in higher dimensions. Finally, we discuss the global structure of such solutions and possible applications.     

A new auxiliary equation method and its application to the Sharma-Tasso-Olver model

A new auxiliary equation method, constructed by a first order nonlinear ordinary differential equation with at most an eighth-degree nonlinear term, is first proposed for exploring more exact solutions to nonlinear evolution equations. Being concise and straightforward, the method, with the aid of symbolic computation, is applied to the Sharma-Tasso-Olver model, and some new exact solitary wave solutions are obtained. The approach is also applicable to searches for exact solutions of other nonlinear evolution equations.     

MΦller＇s Energy of Kerr-NUT Metric

The energy distribution of the Kerr-NUT （Newman-Unti-Tamburino） spacetime is calculated using MΦller＇s energy-momentum complex within the framework of the Riemannian geometry.     

Dixon's extended bodies and impulsive gravitational waves

The “reaction” of an extended body to the passage of an exact plane gravitational wave is discussed following Dixon's model. The analysis performed shows several general features, e.g. even if initially absent, the body acquires a spin induced by the quadrupole structure, the center of mass moves from its initial position, as well as certain “spin-flip” or “spin-glitch” effects which are being observed.     

Regular Charged Solutions in Mφller＇s Tetrad Theory of Gravitation

We find the most general tetrads which give a regular charged spacetime in tetrad theory of gravitation. The metric is a static one and it includes the Schwarzschild and Fteissner Nordstrom black holes. The energy content contained in a sphere of radius R is calculated using the superpotential given by Mφller in the context of Weitzenbock spacetime.     

Equation of motion of small bodies in relativity

There is proven a theorem, to the effect that a material body in general relativity, in a certain limit of sufficiently small size and mass, moves along a geodesic.     

An effective method for finding special solutions of nonlinear differential equations with variable coefficients

There are many interesting methods can be utilized to construct special solutions of nonlinear differential equations with constant coefficients. However, most of these methods are not applicable to nonlinear differential equations with variable coefficients. A new method is presented in this Letter, which can be used to find special solutions of nonlinear differential equations with variable coefficients. This method is based on seeking appropriate Bernoulli equation corresponding to the equation studied. Many well-known equations are chosen to illustrate the application of this method.     

Metric-affine f(R) theories of gravity

General Relativity assumes that spacetime is fully described by the metric alone. An alternative is the so called Palatini formalism where the metric and the connections are taken as independent quantities. The metric-affine theory of gravity has attracted considerable attention recently, since it was shown that within this framework some cosmological models, based on some generalized gravitational actions, can account for the current accelerated expansion of the universe. However we think that metric-affine gravity deserves much more attention than that related to cosmological applications and so we consider here metric-affine gravity theories in which the gravitational action is a general function of the scalar curvature while the matter action is allowed to depend also on the connection which is not a priori symmetric. This general treatment will allow us to address several open issues such as: the relation between metric-affine f(R) gravity and General Relativity (in vacuum as well as in the presence of matter), the implications of the dependence (or independence) of the matter action on the connections, the origin and role of torsion and the viability of the minimal-coupling principle.     

Multi-order exact solutions to the Drinfel'd-Sokolov-Wilson equations

In this Letter, based on the Lamé function and Jacobi elliptic function, the perturbation method is applied to the classical Drinfel'd-Sokolov-Wilson (hereafter DSW for short) equations, and many multi-order solutions are derived. It is shown that different Lamé functions can exist in the first order solutions of DSW system.     

New Lamé function and its application to nonlinear equations

In this Letter, a new kind of Lamé functions are given. Based on the new Lamé functions and Jacobi elliptic function, the perturbation method is applied to the nonlinear equations, and many multi-order solutions of novel forms are derived. In addition, it is shown that different Lamé functions can exist in the first order solutions of nonlinear system.     

Spinning fluid cosmology

The dynamics of a spinning fluid in a flat cosmological model is investigated. The space–time is itself generated by the spinning fluid which is characterized by an energy–momentum tensor consisting a sum of the usual perfect-fluid energy–momentum tensor and some Belinfante–Rosenfeld tensors. It is shown that the equations of motion admit a solution for which the fluid four-velocity and four-momentum are not co-linear in general. The momentum and spin densities of the fluid are expressed in terms of the scale factor.     

Weyl metrics and the generating conjecture

By means of the Ernst complex potential formalism it is shown that previously studied static axially symmetric Einstein-Maxwell fields obtained though the application of the Horsky-Mitskievitch generating conjecture represent a combination of Kinnersley’s transformations [W. Kinnersley: J. Math. Phys.14 (1973) 651]. New theoretical background for the conjecture is suggested and commented.     

Nearly everywhere flat spaces

We discuss some spacetimes, which are flat everywhere except for a thin shell of matter or a string of matter, in the framework of the Israel formalism. First we study spherically symmetric universes with a single sheet of matter. Then we show that the construction of a cosmic string as a limit of various thin shell distributions of matter leads to identical results.     

A Parametric Dynamic Model of Dark Energy

The double complex symmetric gravitational theory is extended to the parametric symmetric gravitational theory by introducing a parameter β. Hence parametric Friedmann-Robertson-Walker equations are obtained and some characters of dark energy in corresponding spaces are discussed by taking different values of β. In our method some previous results can be included as the special case of our results. It is worth noting that some characters of dark energy can be more intuitively described in our model. By analysis, we can predict that the fate of universe would be a Big Rip in the future, and also find that the state parameters for the two different constraint conditions wФ are consistent with the present cosmological observations.