International Journal of Geometric Methods in Modern Physics

In this paper, we present two viscous models of non-perfect fluid by avoiding the introduction of exotic dark energy. We consider the first model in terms of deceleration parameter $q$ has a viscosity of the form $\zeta ={\zeta }_0+({\zeta }_1-{\zeta }_{2}q)H$ and the other model in quadratic form of $H$ of the type $\zeta ={\zeta }_0+{\zeta }_{1}H+{\zeta }_2{H}^2$. In this framework we find the solutions of field equations by using inhomogeneous equation of state of form $p=\omega \rho +\mathrm{\Lambda }(t)$ with equation of state parameter $\omega$ is constant and $\omega (\rho )=b_0{\rho }^{\alpha -1}$.

In this work, we define twisted surfaces in Galilean 3-space. In order to construct these surfaces, a planar curve is subjected to two simultaneous rotations, possibly with different rotation speeds. The existence of Euclidean rotations and isotropic rotations leads to three distinct types of twisted surfaces in Galilean 3-space. Then we classify twisted surfaces in Galilean 3-space with zero Gaussian curvature or zero mean curvature.

A hierarchy of generalized Jaulent–Miodek (JM) equations related to a new spectral problem with energy-dependent potentials is proposed. Depending on the Lax matrix and elliptic variables, the generalized JM hierarchy is decomposed into two systems of solvable ordinary differential equations. Explicit theta function representations of the meromorphic function and the Baker–Akhiezer function are constructed, the solutions of the hierarchy are obtained based on the theory of algebraic curves.

The paper aims to initiate a systematic study of conformal mappings between Finsler spacetimes and, more generally, between pseudo-Finsler spaces. This is done by extending several results in pseudo-Riemannian geometry which are necessary for field-theoretical applications and by proposing a technique that reduces some problems involving pseudo-Finslerian conformal vector fields to their pseudo-Riemannian counterparts. Also, we point out, by constructing classes of examples, that conformal groups of flat (locally Minkowskian) pseudo-Finsler spaces can be much richer than both flat Finslerian and pseudo-Euclidean conformal groups.

In this paper, we investigated the effects of a noncommutative (NC) space-time on the dynamics of the Universe. We generalize the black hole entropy for a NC black hole. Then, using the entropic gravity formalism, we will show that the noncommutativity changes the strength of the gravitational field. By applying this result to a homogeneous and isotropic Universe containing nonrelativistic matter and a cosmological constant, we show that the modified scenario by the noncommutativity of the space-time is a better fit to the obtained data than the standard one at 68% CL.

Nonlinear realizations of the $SO(4,2)$ group are discussed from the point of view of symmetries. Dynamical symmetry breaking is introduced. One linear and one quadratic model in curvature are constructed. Coherent states of the Klauder–Perelomov type are defined for both cases taking into account the coset geometry. A new spontaneous compactification mechanism is defined in the subspace invariant under the stability subgroup. The physical implications of the symmetry rupture in the context of nonlinear realizations and direct gauging are analyzed and briefly discussed.

In this paper, we present a classification of the Kantowski–Sachs spacetime metric according to its conformal Ricci collineations (CRCs). Solving the CRC equations, it is shown that the Kantowski–Sachs metric admits 15-dimensional Lie algebra of CRCs when its Ricci tensor is non-degenerate and an infinite dimensional group of CRCs when the Ricci tensor is degenerate. Some examples of Kantowski–Sachs metric admitting nontrivial CRCs are presented and their physical interpretation is provided.

The objective of the present paper is to study weakly Ricci symmetric spacetimes. Among others, we prove that a weakly Ricci symmetric spacetime obeying Einstein’s field equation without cosmological constant represents stiff matter. Moreover, it is shown that the local cosmological structure of a weakly Ricci symmetric perfect fluid spacetime can be identified as Petrov type $I$, $D$ or $O$. Next, we prove that a dust and dark fluid weakly Ricci symmetric spacetime satisfying Einstein’s field equation without cosmological constant is vacuum. Finally, we show the non-existence of radiation era in such a spacetime.

We give a complete description, provided with a mathematical proof, of the shape of the spectrum of the Hill operator with potential $4{cos}^{2}x+4iVsin2x$, where $V\in (0,\infty ).$ We prove that the second critical point $V_2$, after which the real parts of the first and second bands disappear, is a number between $0.8884370025$ and $0.8884370117$. Moreover, we prove that $V_2$ is the degeneration point for the first periodic eigenvalue. Besides, we give a scheme by which one can find arbitrary precise value of the second critical point as well as the $k$th critical points after which the real parts of the $(2k-3)$th and $(2k-2)$th bands disappear, where $k=3,4,\dots .$

In this paper, we will study the Lorentz symmetry breaking down to its subgroup. A two-form gauge theory is investigated in the Lorentz violating background and it will be shown that this symmetry violation affects the structure of this gauge theory. In particular, we will study the gaugeon formalism and FFBRST for such a theory in this broken spacetime. In addition to Kugo-Ojima type condition, a thorough evaluation of quantum gauge freedom and gaugeon modes is carried out. We will explicitly demonstrate that in Lorentz broken spacetime, our reducible gauge theory fully depicts the physical aspects of gaugeon fields.

A warm inflation model, drawn upon the vector cosmology, was applied in the present work to calculate cosmological fluctuations. Moreover, parameters of the model were constrained and compared using the latest observational data such as Planck and WMAP9.

We study the existence and stability criteria for circular geodesics of spherically symmetric tidal-charged black hole (BH). We investigate in details the equatorial causal geodesics of the tidal-charged BH in comparison with spherically symmetric Reissner–Nordström BH spacetime. We particularly focused on both the null circular geodesics and time-like circular geodesics. Using the effective potential diagram, we have compared the geodesic structure between two spacetimes. We have derived the ISCO (innermost stable circular orbit), MBCO (marginally bound circular orbit) and CPO (circular photon orbit) for both the spacetimes. Moreover, we have derived the quasi-normal modes$($QNMs$)$ frequency in the eikonal limit for both the spacetimes via Lyapunov exponent. In the appendix section, we have shown that a spherically symmetric tidal-charged BH can act as particle accelerators with ultra-high center-of-mass (CM) energy in the limiting case of maximal BH tidal-charge$(q)$ and it is possible when two neutral particles are colliding near the horizon.

The aim of the present paper is to investigate conformal changes in absolute parallelism geometry. We find out some new conformal invariants in terms of the Weitzenböck connection and the Levi-Civita connection of an absolute parallelism space.

We present the notion of a filtered bundle as a generalization of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more general polynomial transformation laws. The key examples of such bundles include affine bundles and various jet bundles, both of which play fundamental roles in geometric mechanics and classical field theory. We also present the notion of double filtered bundles which provide natural generalizations of double vector bundles and double affine bundles. Furthermore, we show that the linearization of a filtered bundle — which can be seen as a partial polarization of the admissible changes of local coordinates — is well defined.

Three new cosmological models of the present Universe are obtained with $f(R,T)$ modified theory of gravity proposed by Harko et al. [Phys. Rev. D 84 (2011) 024020, arXiv:1104.2669 [gr-qc]] in a general class of Bianchi space-time. In this paper, we have generalized the modified $f(R,T)$ field equations with $\mathrm{\Lambda }(T)$-gravity, where $R$ and $T$ denote the curvature scalar and the trace of the stress–energy–momentum tensor, respectively. To find the deterministic solutions we have considered the linearly varying deceleration parameter $q$ proposed by Akarsu and Dereli [Cosmological models with linearly varying deceleration parameter, Int. J. Theor. Phys. 51 (2011) 612]. We have made the analyses of the variation of pressure, energy density and cosmological term with cosmic time. It is observed that our derived models are unstable in early time whereas they are stable at late and future time (i.e. at present epoch). The physical and geometric properties of all three models are studied in detail.

Let $G$ be a Lie group equipped with a left invariant Randers metric of Berward type $F$, with underlying left invariant Riemannian metric $g$. Suppose that $\tilde{F}$ and $\tilde{g}$ are lifted Randers and Riemannian metrics arising from $F$ and $g$ on the tangent Lie group $TG$ by vertical and complete lifts. In this paper, we study the relations between the flag curvature of the Randers manifold $(TG,\tilde{F})$ and the sectional curvature of the Riemannian manifold $(G,g)$ when $\tilde{F}$ is of Berwald type. Then we give all simply connected three-dimensional Lie groups such that their tangent bundles admit Randers metrics of Berwarld type and their geodesics vectors.

A Bianchi type II cosmological model with expansion and rotation has been constructed. The model describes the Friedmannian stage of the Universe’s evolution including a subsequent transition to the accelerated exponential expansion observed nowadays. The gravitational field sources of the model are an ultra-relativistic matter, dust and co-moving anisotropic rotating dark energy. The possibility of detecting the cosmological rotation by astrophysical observations is discussed.