International Journal of Geometric Methods in Modern Physics

In this paper, we have proposed a new form for the varying deceleration parameter that is a generalization of the form of Ö. Akarsu and T. Dereli [Cosmological models with linearly varying deceleration parameter, Int. J. Theor. Phys. 51(2012) 612]. LRS Bianchi type-I cosmological model filled with a perfect fluid source in $f(R,T)$ gravity theory, where $R$ is the Ricci scalar and $T$ is the trace of the stress energy–momentum tensor, has been studied in order to investigate early time deceleration and late time acceleration of the universe by using this new form of time-varying deceleration parameter. The time evolution of physical and dynamical parameters have been analyzed and shown by graphs. Moreover, the deceleration parameter has been considered in terms of redshift. It has been shown that the model starts with a big bang and ends with a big rip. It is filled by a quintessence like fluid at the early time and by a phantom like fluid at the late time.

We introduce two types of mappings that preserve nonnull helices in Minkowski spaces. The first type constructs helices in the $n$-dimensional Minkowski space from helices in the same Minkowski space. The second type constructs helices in the $(n+1)$-dimensional Minkowski space from helices in the $n$-dimensional Minkowski space. Furthermore, we study invariants of these mappings and present examples.

In this work, the quadratic helicity ${\chi }_{\bar{B}}^{(2)}$ is discussed from the physical and topological points of view. We show, after the introduction of a mathematical description of the properties of helicity and quadratic helicity in the context of standard dynamo equations, examples of the importance of these high invariants in cosmological scenarios. These scenarios consider extensions of the standard model and extensions of GR.

In this paper, we examine the wormhole solutions by taking two different anisotropic models in Rastall gravity. For this purpose, we shall discuss anisotropic fluid to construct two different anisotropic models. Further, we shall employ two specific shape functions to calculate the behavior of energy conditions. The presence of exotic matter is confirmed in all the cases of this study due to the violation of the null energy condition. All the properties of shape function under both anisotropic models are fulfilled. It is noticed that wormhole solutions exist under the particular values of involved parameters in different cases in Rastall gravity.

In this paper, we classify proper non-static cylindrically symmetric (CS) perfect fluid space-times via conformal vector fields (CVFs) in the $f(R)$ gravity. In order to classify the space-times, we use the algebraic and direct integration approaches. In the process of classification, there exist 23 cases for which the considered space-times become proper non-static. By studying each case in detail, we find that the conformal vector fields are of dimensions two, three and fifteen in the $f(R)$ gravity.

In this paper, we have studied the propagation of cylindrical shock waves in a self-gravitating perfect gas under the influence of azimuthal magnetic field. The method of Lie group invariance is used to construct some special class of self-similar solutions in the presence of the azimuthal magnetic field. The different cases of solutions with a power law and exponential law shock paths are obtained with the choice of arbitrary constants appearing in the expressions for the infinitesimal generators. The similarity solution for cylindrical shock wave with power law shock path is discussed in detail. The effects of variation of Alfven-Mach number, gravitation parameter, initial density variation index and adiabatic exponent on the flow variables are analyzed graphically. It is obtained that the increase in the values of Alfven-Mach number, gravitation parameter and adiabatic exponent have decaying effect on the shock strength. Also, the shock strength increases with an increase in the values of initial density variation index. A comparison is also made between the solutions in gravitating and non-gravitating cases in the presence of magnetic field.

The aim of this paper is to investigate the conformal vector fields (CVFs) for some vacuum classes of static spherically symmetric space-times in $f(T,B)$ gravity. First, we have explored the space-times by solving the Einstein field equations in $f(T,B)$ gravity. These solutions have been obtained by imposing various conditions on the space-time components and selecting separable form of the bivariate function $f(T,B)$. Second, we find the CVFs of the obtained space-times via direct integration approach. The overall study reveals that there exist 17 cases. From these 17 cases, the space-times in five cases admit proper CVFs whereas in rest of the 12 cases, CVFs become Killing vector fields (KVFs). We have also calculated the torsion scalar and boundary term for each of the obtained solutions.

We derive a necessary and sufficient condition for Poincaré Lie superalgebras in any dimension and signature to be isomorphic. This reduces the classification problem, up to certain discrete operations, to classifying the orbits of the Schur group on the vector space of superbrackets. We then classify four-dimensional ${𝒩}=2$ supersymmetry algebras, which are found to be unique in Euclidean and in neutral signature, while in Lorentz signature there exist two algebras with R-symmetry groups $\mathrm{\text{U}}(2)$ and $\mathrm{\text{U(}}1,1)$, respectively.

Following the classification up to isomorphism of ${𝒩}=2$ Poincaré Lie superalgebras in four dimensions with arbitrary signature obtained in a companion paper, we present off-shell vector multiplet representations and invariant Lagrangians realizing these algebras. By dimensional reduction of five-dimensional off-shell vector multiplets, we obtain two representations in each four-dimensional signature. In Euclidean and neutral signature, these representations can be mapped to each other by a field redefinition induced by the action of the Schur group on the space of superbrackets. In Minkowski signature, we show that the superbrackets underlying the two vector multiplet representations belong to distinct open orbits of the Schur group and are therefore inequivalent. Our formalism allows to answer questions about the possible relative signs between terms in the Lagrangian systematically by relating them to the underlying space of superbrackets.

The results of two space experiments, around the world clocks and gravity probe B, are analyzed theoretically using a field theory. The field equations of this theory are reduced to those of general relativity outside material distribution, while its equations of motion are not a geodesic one. This equation violates the weak equivalence principle because of the non-vanishing torsion in the geometry used. The predictions of the theory give rise to the time dilation measured by the first experiment and to the geodetic and frame drag effects measured by the second experiment. Furthermore, we show that these predictions are affected by the torsion of space-time. The torsion term, in the equation of motion, is connected to other effects through a coupling parameter. This parameter is called the “spin-torsion” coupling if the moving test particle is elementary one with non-vanishing quantum spin. We call this parameter “rotation-torsion” coupling if the moving test particle is a gyroscope. In the first case, the coupling parameter is well defined and confirmed by terrestrial experiment, while in the second case the parameter still needs further investigation and discussion.

We characterize almost co-Kähler manifolds with gradient Yamabe, gradient Einstein and quasi-Yamabe solitons. It is proved that if the metric of a $(\kappa ,\mu )$-almost co-Kähler manifold $M^{2n+1}$ is a gradient Yamabe soliton, then $M^{2n+1}$ is either $K$-almost co-Kähler or $N(\kappa )$-almost co-Kähler or the metric of $M^{2n+1}$ is a trivial gradient Yamabe soliton. A $(\kappa ,\mu )$-almost co-Kähler manifold with gradient Einstein soliton is $K$-almost co-Kähler. Finally, it is shown that an almost co-Kähler manifold admitting a quasi-Yamabe soliton, whose soliton vector is pointwise collinear with the Reeb vector field of the manifold, is $K$-almost co-Kähler. Consequently, some results of almost co-Kähler manifolds are deduced.

We construct the $q$-deformed fuzzy Dirac and chirality operators on quantum fuzzy Podles sphere $S_{q\mu }^2$. We will show that there are a class of these operators on $S_{q\mu }^2$ in which all of them in the limit case $q\to 1$ has the correct fuzzy sphere limit as well as they have correct commutative limit in the limit case when $q\to 1$ and noncommutative parameter $l$ tends to infinity.

In this paper, we study the quantum-corrected and generalizedf uncertinty principle (GUP)-corrected thermodynamics of the $(2+1)$-dimensional charged-rotating Achucarro–Ortiz (AO) black hole. The corrected parameters include temperature, entropy, and heat capacity which help to investigate the instability phases of the Achucarro–Ortiz black hole. We show that this black hole with small mass possesses unstable regions. However, we reveal that those instabilities can be removed by the GUP corrections. Finally, we also compute the maximum temperature that can be reached by the Achucarro–Ortiz black hole. We show that corrected temperatures by different methods we used are identical at the small mass limit, hence GUP correction at small mass limit is a quantum gravity correction. Interestingly, we show by graphical analysis that leading-order quantum-corrected temperature of the Achucarro–Ortiz black hole behaves similar to the GUP-corrected temperature of uncharged Achucarro–Ortiz black hole.

We argue that in a framework for emergent quantum mechanics, the weak equivalence principle is a consequence of concentration of measure in large-dimensional spaces of $1$-Lipshitz functions. Furthermore, as a consequence of the emergent framework and the properties that we assume for the fundamental dynamics, it is argued that gravity must be a classical, emergent interaction.

In this paper, we have studied the transition and physical behavior of Bianchi type-V cosmological models within the formalism of $f(R,T)$ gravity. To obtain the solution of field equations and phase transition of universe consistent with recent cosmological observations, time varying deceleration parameters are considered. In this paper, we used two different scale factors of the form (i) $a={(t^m{e}^{\beta t})}^{1/n}$, where $n\ge 0,m\ge 0,\beta \ge 0$ are constants. Here, for $n\ge 2,$ the universe shows transition with accelerated expansion. (ii) $a={(sinh\beta t)}^{1/n}$, where $n\ge 0$ and $\beta \ge 0$ are constants. For $n\ge 2.5$, the universe achieves a phase transition from early decelerating to current accelerating phase. The model I initially starts with quintessence scenario ($\omega >-1$) and ends up with ($\omega =-1$) as a model with cosmological constant ($\mathrm{\Lambda }$) as $t\to \infty$. Model II, for $n=2.5$ indicates the phantom energy scenario and for $n\ge 3$, the model starts with quintessence $\omega >-1$ and ends with vacuum energy scenario. A point type singularity has been observed in the derived model I. Some physical and geometrical properties of the models have been established and discussed to derive the validity of models with respect to recent astrophysical observations.

In this paper, we study spatially homogeneous and anisotropic Bianchi type-V and IX universes filled with interacting dark matter and holographic dark energy. We obtained the solution of the field equations by using the variable deceleration parameter in the form $R(t)=t^{\delta }{e}^{\gamma t}$. The cosmological parameters of the models like deceleration and equation of state are obtained. We observe that the deceleration parameter tends to $-1$ which shows an accelerated universe, and the equation of state tends to $-1$ which belongs to $\mathrm{\Lambda }$CDM model. Moreover, we establish the correspondence between holographic dark energy model and quintessence scalar field.