A new class of plane symmetric solution

A new class of static plane symmetric solution of Einstein field equation generated by a perfect fluid source is put forward. A special family of this new solution is investigated in detail. The constraints on the parameters by different energy conditions are studied. The classical stability of this solution is discussed. The junction conditions matching to Minkowski metric and Taub metric are analyzed respectively.     

Non-Spherical Gravitational Collapse of Strange Quark Matter

We study the non-spherical gravitational collapse of the strange quark null fluid. The interesting feature which emerges is that the non-spherical collapse of charged strange quark matter leads to a naked singularity whereas the gravitational collapse of neutral quark matter proceeds to form a black hole. We extend the earlier work of Harko and Cheng [Phys. Lett. A 266 （2000） 249] to the non-spherical case.     

A global conformal extension theorem for perfect fluid Bianchi space-times

A global extension theorem is established for isotropic singularities in polytropic perfect fluid Bianchi space-times. When an extension is possible, the limiting behaviour of the physical space-time near the singularity is analysed.     

Exact self-gravitating N-body motion in the CGHS model

In the asymptotically flat two-dimensional dilaton gravity, we present an N-body particle action which has a dilaton coupled mass term for the exact solubility. This gives nonperturbative exact solutions for the N-body self-gravitating system, so the infalling particles form a black hole and their trajectories are exactly described. In our two-dimensional case, the critical mass for the formation of black holes does not exist, so even a single particle forms a black hole. The infalling particles give additional time-like singularities in addition to the space-like black hole singularity. However, the latter singularities can be properly cloaked by the future horizons within some conditions.     

Conjecture on Avoidance of Big Crunch

By conjecturing the physics at the Planck scale, we modify the definition of the Hawking temperature and modify the Friedmann equation. It is found that we can avoid the singularity of the big crunch and obtain a bouncing cosmological model.     

Exact self-gravitating N-body motion in the CGHS model

In the asymptotically flat two-dimensional dilaton gravity, we present an N-body particle action which has a dilaton coupled mass term for the exact solubility. This gives nonperturbative exact solutions for the N-body self-gravitating system, so the infalling particles form a black hole and their trajectories are exactly described. In our two-dimensional case, the critical mass for the formation of black holes does not exist, so even a single particle forms a black hole. The infalling particles give additional time-like singularities in addition to the space-like black hole singularity. However, the latter singularities can be properly cloaked by the future horizons within some conditions.     

Gravitating discs around a Schwarzschild black hole II

A sequence of exact spacetimes is obtained describing the fields of a Schwarzschild black hole surrounded by stable static axisymmetric thin discs having their inner rim at the least possible radius. In the previous paper we only required stability with respect to perturbations in the disc plane, while it turns out that for discs with relative mass >0.23 the perturbations in perpendicular direction are more dangerous. The discs of the resulting sequence have their inner rims just on, or very close to, circular geodesics marginally stable with respect to either of the perturbations. Redshift from static and Keplerian observers in the disc is computed. The inverted first Morgan-Morgan counter-rotating disc, used in superpositions, has a number of satisfactory physical properties, but it has turned out to have a curvature singularity at the inner rim. However, this is only a consequence of a too steep radial start of density, not present in (inverted) “higher” Morgan-Morgan solutions. Dedicated to Professor Jiří Bičák on the occasion of his 60th birthday.     

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.     

Entropy of an extremal regular black hole

We introduce a magnetically charged extremal regular black hole in the coupled system of Einstein gravity and nonlinear electrodynamics. Its near horizon geometry is given by AdS₂×S²${\mathit{AdS}}_2\times S^2$. It turns out that the entropy function approach does not automatically lead to a correct entropy of the Bekenstein–Hawking entropy. This contrasts to the case of the extremal Reissner–Norström black hole in the Einstein–Maxwell theory. We conclude that the entropy function approach does not work for a magnetically charged extremal regular black hole without singularity, because of the nonlinearity of the entropy function.     

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.     

Bouncing cosmologies

We review the general features of nonsingular universes (i.e. those that go from an era of accelerated collapse to an expanding era without displaying a singularity) as well as cyclic universes. We discuss the mechanisms behind the bounce, and analyze examples of solutions that implement these mechanisms. Observational consequences of such regular cosmologies are also considered, with emphasis in the behavior of perturbations.     

Bulk viscous L.R.S. Bianchi type V tilted stiff fluid cosmological model in general relativity

Locally rotationally symmetric (L.R.S.) Bianchi type V bulk viscous tilted stiff fluid cosmological model is investigated. To get the deterministic model of the universe, we have also assumed a condition A=Bⁿ between metric potentials A, B where n is the constant. The behaviour of the model in presence and absence of bulk viscosity and singularities in the model are also discussed. In general, the models represent accelerating, shearing, tilted and non-rotating universe. The models have point type singularity in presence and absence of bulk viscosity both.     

Gravitational Collapse of Radiating Dyon Solution and Cosmic Censorship Hypothesis

We investigate the possibility of cosmic censorship violation in the gravitational collapse of radiating dyon solution. It is shown that the final outcome of the collapse depends sensitively on the electric and magnetic charge parameters. The graphs of the outer apparent horizon, inner Cauchy horizon for different values of parameters are drawn. It is found that the electric and magnetic components push the apparent horizon towards the retarded time-coordinate axis, which in turn reduces the radius of the apparent horizon in Valdya spacetime. Also, we extend the earlier work of Chamorro and Virbhadra [Pramana, J. Phys. 45 （1995） 181].     

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.     

Taub–NUT black holes in third order Lovelock gravity

We consider the existence of Taub–NUT solutions in third order Lovelock gravity with cosmological constant, and obtain the general form of these solutions in eight dimensions. We find that, as in the case of Gauss–Bonnet gravity and in contrast with the Taub–NUT solutions of Einstein gravity, the metric function depends on the specific form of the base factors on which one constructs the circle fibration. Thus, one may say that the independence of the NUT solutions on the geometry of the base space is not a robust feature of all generally covariant theories of gravity and is peculiar to Einstein gravity. We find that when Einstein gravity admits non-extremal NUT solutions with no curvature singularity at r=N$r=N$, then there exists a non-extremal NUT solution in third order Lovelock gravity. In 8-dimensional spacetime, this happens when the metric of the base space is chosen to be CP³${\mathbb{CP}}^3$. Indeed, third order Lovelock gravity does not admit non-extreme NUT solutions with any other base space. This is another property which is peculiar to Einstein gravity. We also find that the third order Lovelock gravity admits extremal NUT solution when the base space is T²×T²×T²$T^2\times T^2\times T^2$ or S²×T²×T²$S^2\times T^2\times T^2$. We have extended these observations to two conjectures about the existence of NUT solutions in Lovelock gravity in any even-dimensional spacetime.     

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.     

New Symmetries for a Model of Fast Diffusion

The new symmetries for a mathematical model of fast diffusion are determined. A new system method is given to search for new symmetries of differential equations written in a conserved form, several new symmetry generators and exact solutions are presented.     

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.     

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.