On isoperimetric surfaces in general relativity,II

We determine the optimal way to enclose volume in a class of domains inside certain Friedmann–Robertson–Walker metrics. The method employed is an adaptation of the Bray–Morgan isoperimetric comparison procedure to the Lorentzian setting. We also make some remarks on isoperimetric comparison in the Riemannian setting, for rotationally-symmetric space-like slices in non-vacuum space-times.     

The exact behavior of electromagnetic Faraday rotation in crossing a gravitational sandwich wave in general relativity

We have analyzed the exact behavior of the polarization vector of a linearly polarized electromagnetic shock wave upon crossing a gravitational sandwich wave, by using Einstein's theory of general relativity. The Faraday rotation in the polarization vector of the electromagnetic field is induced in this nonlinear process. We show that the Faraday's angle highly depends on the electromagnetic parameter, gravitational parameter and the width of the gravitational sandwich wave.     

General relativistic Boltzmann equation, I: Covariant treatment

This series of two articles aims at dissipating the rather dense haze existing in the present literature around the General Relativistic Boltzmann equation. In this first article, the general relativistic one-particle distribution function in phase space is defined as an average of delta functions. Thereupon, the general relativistic Boltzmann equation, to be obeyed by this function, is derived. The use of either contravariant or covariant momenta leads to different, but equivalent, forms of the equation.The results of the present article are covariant, but not manifestly covariant. The transition to a manifestly covariant treatment, on the basis of off-shell momenta, is given in the second article.     

General relativistic Boltzmann equation, II: Manifestly covariant treatment

In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p²=m²c². Due to this restriction, the resulting Boltzmann equation, although covariant, turned out to be not manifestly covariant. In the present article we switch from mass-shell momenta to off-shell momenta, and thereby arrive at a Boltzmann equation that is manifestly covariant.     

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.     

Generalised Chern–Simons actions for 3d gravity and κ-Poincaré symmetry

We consider Chern–Simons theories for the Poincaré, de Sitter and anti-de Sitter groups in three dimensions which generalise the Chern–Simons formulation of 3d gravity. We determine conditions under which κ-Poincaré symmetry and its de Sitter and anti-de Sitter analogues can be associated to these theories as quantised symmetries. Assuming the usual form of those symmetries, with a timelike vector as deformation parameter, we find that such an association is possible only in the de Sitter case, and that the associated Chern–Simons action is not the gravitational one. Although the resulting theory and 3d gravity have the same equations of motion for the gauge field, they are not equivalent, even classically, since they differ in their symplectic structure and the coupling to matter. We deduce that κ-Poincaré symmetry is not associated to either classical or quantum gravity in three dimensions. Starting from the (non-gravitational) Chern–Simons action we explain how to construct a multi-particle model which is invariant under the classical analogue of κ-de Sitter symmetry, and carry out the first steps in that construction.     

Ultrasmall Double Junction in Terms of Orthogonal Polynomials

The issue of the form that the energy tensor of the electromagnetic field should be given in matter is reconsidered, and the neat derivation of Abraham’s tensor once provided by W. Gordon is recollected. In order to extend to the high frequency domain the experimental evidence gathered up to now in favour of Abraham’s tensor, a method for detecting the Abraham’s force supposedly exerted by light on a transparent, homogeneous medium is outlined. It avails of the Fresnel-Fizeau effect associated with the motion of matter that should be caused by the above mentioned force.     

On the supersymmetric limit of Kerr-NUT-AdS metrics

Generalizing the scaling limit of Martelli and Sparks [D. Martelli, J. Sparks, Phys. Lett. B 621 (2005) 208, hep-th/0505027] into an arbitrary number of spacetime dimensions we re-obtain the (most general explicitly known) Einstein–Sasaki spaces constructed by Chen et al. [W. Chen, H. Lü, C.N. Pope, Class. Quantum Grav. 23 (2006) 5323, hep-th/0604125]. We demonstrate that this limit has a well-defined geometrical meaning which links together the principal conformal Killing–Yano tensor of the original Kerr-NUT-(A)dS spacetime, the Kähler 2-form of the resulting Einstein–Kähler base, and the Sasakian 1-form of the final Einstein–Sasaki space. The obtained Einstein–Sasaki space possesses the tower of Killing–Yano tensors of increasing rank—underlined by the existence of Killing spinors. A similar tower of hidden symmetries is observed in the original (odd-dimensional) Kerr-NUT-(A)dS spacetime. This rises an interesting question whether also these symmetries can be related to the existence of some ‘generalized’ Killing spinor.     

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.     

Moving curves of the sine-Gordon equation: New links

We provide a general scheme for mapping integrable nonlinear partial differential equations of real functions to moving space curves using an approach different from the one proposed by Lamb. We apply our method to the sine-Gordon equation and obtain links to five new classes of space curves, in addition to the two found by Lamb. For each class, we display the rich variety of moving curves associated with the one-soliton, the breather, the two-soliton and the soliton-antisoliton solutions, and suggest possible applications. Our results also provide new insights with regard to the two-soliton (soliton-antisoliton) scattering process.     

Intrinsic geometry of curves and the Lorentz equation

We show that the trajectory of a point charge in a uniform electromagnetic field is a helix if the Lorentz equation governs its motion. Our approach is totally relativistic, and it is based on the use of the Frenet-Serret formulae which describe the intrinsic geometry of world lines in Minkowski 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.     

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.     

Quantum anticentrifugal force for wormhole geometry

We show the existence of an anticentrifugal force in a wormhole geometry in R³. This counterintuitive force was shown to exist in a flat R² space. The role the geometry plays in the appearance of this force is discussed.     

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.     

On the two approaches to the data analysis of the Cassini interplanetary relativity experiment

We compare two theoretical approaches to the data analysis of the Cassini relativity experiment based on the Doppler tracking and the time delay technique that were published correspondingly by Kopeikin et al. [S.M. Kopeikin, A.G. Polnarev, G. Schäfer, I.Yu. Vlasov, Phys. Lett. A 367 (2007) 276] and by Bertotti et al. [B. Bertotti, N. Ashby, L. Iess, Class. Quantum Grav. 25 (2008) 045013]. Bertotti et al. believed that they found a discrepancy with our paper and claimed that our analysis was erroneous. The present Letter elucidates, however, that the discrepancy is illusory and does not exist. The two techniques give the same result making it evident that the numerical value of the PPN parameter γ measured in the Cassini experiment is indeed affected by the orbital motion of the Sun around the barycenter of the solar system.     

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.     

Higher Dimensional Strange Quark Matter Coupled to the String Cloud with Electromagnetic Field Admitting One Parameter Group of Conformal Motion

We solve Einstein＇s field equations in higher-dimensional spherically symmetric spacetime with strange quark matter attached to the string cloud, assuming one parameter group of con formal motions. The solutions match with the higher-dimensional Reissner-Nordstroem metric on the boundary at r=ro. The features of the solutions are also discussed in the framework of higher-dimensional spacetime.