International Journal of Geometric Methods in Modern Physics

The paper aims to apply the octonions to explore the precessional angular velocities of several particles in the electromagnetic and gravitational fields. Some scholars utilize the octonions to research the electromagnetic and gravitational fields. One formula can be derived from the octonion torque, calculating the precessional angular velocity generated by the gyroscopic torque. When the octonion force is equal to zero, it is able to deduce the force equilibrium equation and precession equilibrium equation and so forth. From the force equilibrium equation, one can infer the angular velocity of revolution for the particles. Meanwhile, from the precession equilibrium equation, it is capable of ascertaining the precessional angular velocity induced by the torque derivative, including the angular velocity of Larmor precession. Especially, some ingredients of torque derivative are in direct proportion to the field strengths. The study reveals that the precessional angular velocity induced by the torque derivative is independent of that generated by the torque. The precessional angular velocity, induced by the torque derivative, is relevant to the torque derivative and the spatial dimension of precessional velocity. It will be of great benefit to understanding further the precessional angular velocity of the spin angular momentum.

We show that the asymptotic infinite dimensional enlarged gauge symmetries constructed for QED are anomalous in Weyl semimetals. This symmetry is particularly important in particle physics for its analogy with the Bondi–Metzner–Sachs (BMS) symmetries in gravity, as well as for its connection with QED soft IR theorems. This leads to observable effects, because of the induction of a new current in the material, which carries a memory of the BMS symmetry precursor.

In this paper, we study geometrical properties of marginally trapped surfaces in gravitational collapse, using a semi-tetrad covariant formalism, that provides a set of geometrical and matter variables. We first define a generalization (in a sense to be specified in the introduction) of LRS II spacetime — which we call NNF spacetimes — and show that the marginally trapped surfaces in NNF spacetimes (and the 3-surfaces they foliate) are topologically equivalently those of LRS II spacetimes. We then study the evolution of MTTs (3-surfaces foliated by marginally trapped surfaces), extending earlier work on LRS II spacetimes to NNF spacetimes, and in general any 4-dimensional spacetime. In addition, we perform a stability analysis for the marginally trapped surfaces in this formalism, using simple spacetimes as examples to demonstrate the applicability of our approach.

In this paper, a new form of dark energy, known as Tsallis holographic dark energy (THDE), with IR cutoff as Hubble horizon proposed by Tavayef et al. Tsallis holographic dark energy, Phys. Lett. B 781 (2018) 195 has been explored in Bianchi-III model with the matter. By taking the time subordinate deceleration parameter, the solution of Einstein’s field equation is found. The Universe evolution from earlier decelerated to the current accelerated phase is exhibited by the deceleration parameter acquired in the THDE model. It can be seen that the derived THDE model is related to an accelerating Universe with quintessence ($\omega \ge -1$). The squared sound speed $v_s^2$ also suggests that the THDE model is classically stable at present. In addition, the quintessence phase of the THDE model is analyzed with swampland conjecture to reformulate the accelerating expansion of the Universe.

We study lightlike submanifolds of indefinite statistical manifolds. Contrary to the classical theory of submanifolds of statistical manifolds, lightlike submanifolds of indefinite statistical manifolds need not to be statistical submanifold. Therefore, we obtain some conditions for a lightlike submanifold of indefinite statistical manifolds to be a lightlike statistical submanifold. We derive the expression of statistical sectional curvature and finally obtain some conditions for the induced statistical Ricci tensor on a lightlike submanifold of indefinite statistical manifolds to be symmetric.

We study semi-invariant Riemannian submersions from a nearly Kaehler manifold to a Riemannian manifold. It is well known that the vertical distribution of a Riemannian submersion is always integrable therefore, we derive condition for the integrability of horizontal distribution of a semi-invariant Riemannian submersion and also investigate the geometry of the foliations. We discuss the existence and nonexistence of semi-invariant submersions such that the total manifold is a usual product manifold or a twisted product manifold. We establish necessary and sufficient conditions for a semi-invariant submersion to be a totally geodesic map. Finally, we study semi-invariant submersions with totally umbilical fibers.

In this paper, we study cylindrical helices, Mannheim curves and Darboux developable surfaces associated to Mannheim curves. We give a method for constructing Mannheim curves from spherical curves and demonstrate that all Mannheim curves can be constructed by such a way. We also introduce the spherical Darboux images of Mannheim curves, and we give a classification of singularities of Darboux developable surfaces and spherical Darboux images. Moreover, we study the geometric properties of singularities as applications of singularity theory for spherical curves.

Emergent universe (EU) cosmological models with viscosity in a modified gravity which contains a general function $f(R,T)$, where $R$ and $T$ denote the curvature scalar and the trace of the energy–momentum tensor, respectively, are studied in a flat Friedmann–Robertson–Walker metric. Cosmological solutions are obtained in $f(R,T)$ theory of gravity, which represented as $f(R,T)=f(R)+f(T)$ with bulk viscosity that described by Eckart theory, truncated Israel Stewart theory and full Israel Stewart Theory. The physical and geometrical features of the EU models in $f(R,T)={\alpha }_{1}R+{\lambda }_{1}T$ gravity, where ${\alpha }_1$ and ${\lambda }_1$ are coupling parameters, with bulk viscosity are studied in details. Constraints of the EU models parameters in $f(R,T)$ gravity with bulk viscosity are estimated from observational data set. The stability analysis of the equilibrium points admitting cosmological solutions of the dynamical system associated with the evolution in the modified gravity is studied in Eckart theory, truncated Israel Stewart theory and full Israel Stewart theory.

This study explores the wormhole solutions in $f(𝔾,𝕋)$ Gravity. For this purpose we assume two sorts of matter density profiles, which satisfy the Gaussian and Lorentzian noncommutative distributions. Further, we employ the conformal motions in the back ground of nonzero conformal killing vectors to find the shape-function from the modified field equations of $f(𝔾,𝕋)$ gravity. By defining the connection between Gaussian and Lorentzian noncommutative distributions with conformal Killing vectors, it has been investigated that wormhole solutions would exist under the particular values of involved parameters in $f(𝔾,𝕋)$ gravity.

We propose a new integrable coupled dispersionless equation with self-consistent sources (CDESCS). We obtain the Lax pair and the equivalent generalized Heisenberg ferromagnet equation (GHFE), demonstrating its integrability. Specifically, we explore the geometry of these equations. Last, we consider the relation between the motion of curves/surfaces and the CDESCS and the GHFE.

The aim of this paper, is to study the Riemann soliton and gradient almost Riemann soliton on certain class of almost Kenmotsu manifolds. Also, some suitable examples of Kenmotsu and ${(\kappa ,\mu )}^{\prime }$-almost Kenmotsu manifolds are constructed to justify our results.

We identify the two-dimensional surfaces corresponding to certain solutions of the Liouville equation of importance for mathematical physics, the nontopological Chern–Simons (or Jackiw–Pi) vortex solutions, characterized by an integer $N\ge 1$. Such surfaces, that we call $S^2(N)$, have positive constant Gaussian curvature, $K$, but are spheres only when $N=1$. They have edges, and, for any fixed $K$, have maximal radius $c$ that we find here to be $c=N/\sqrt{K}$. If such surfaces are constructed in a laboratory by using graphene (or any other Dirac material), our findings could be of interest to realize table-top Dirac massless excitations on nontrivial backgrounds. We also briefly discuss the type of three-dimensional spacetimes obtained as the product $S^2(N)\times ℝ$.

In this paper, we have discussed string cosmological model within the framework of $f(R,T)$ theory of gravity in homogeneous but anisotropic Bianchi Type-II space-time. We have considered cosmic string as a source of energy–momentum tensor. We get the solution of the corresponding field equations by assuming deceleration parameter $q(t)=-1+\frac{\beta }{\sqrt{2\beta t+k}}$, which is time-dependent (here, $k$ and $\beta$ are arbitrary constants). This particular form of scale factor enables us to explain the two scenarios, (i) By using recent constraints ($H_0=73.8$, $q_0=-0.73$) from supernovae type Ia union data (Cunha, Kinematic constraints to the transition redshift from supernovae type Ia union data, Phys. Rev. D 79 (2009) 047301), we find the values of arbitrary constants $\beta$ and $k$ for which we have derived a cosmological model showing accelerating expansion universe ($q<0$) only throughout the evolution and (ii) By using the recent constraints ($H_0=73.8$, and $q_0=-0.54$) from SNIa data in combination with BAO and CMB observations (Giostri et al. From cosmic deceleration to acceleration: new constraints from SN Ia and BAO/CMB, J. Cosmol. Astrophys. 3 (2012) 27), we find the values of arbitrary constants for which we have derived a cosmological model with phase transition from early decelerating ($q>0$) to the present accelerating ($q<0$) universe. Also, for the model, we have evaluated and discussed the various physical and kinematic parameters. We have also shown the variation of these cosmological parameters graphically for specific values of the constants. The stability and physical viability are also discussed for the derived models using some recently developed diagnostic tools.

We propose a new model of Lorentz breaking massive gravity in which the mass of the graviton depends from the space-time directions. We explore its consistency: absence of ghosts, tachyons, gradient instabilities, VDVZ discontinuities. We demonstrate that the model is not plagued by any pathology in a large region of parameters space. Within this new theory, we find several interesting phenomena. First of all, gravitational waves propagate an-isotropically in space-time. Second, we find anisotropic corrections to the Newtonian potential, with new extra Yukawa-like phases. Such a scenario also carries intriguing consequences in context of large extra dimensions proposals, as a confinement mechanism of gravity in $3+1$ dimensions.

In this study, we investigate the potential functions $V(x^i)$ that appear in the Lagrangian $L(x^i,\mathrm{\Phi },{\mathrm{\Phi }}_i)=\frac{1}{2}\sqrt{g}{g}^{ij}{\mathrm{\Phi }}_i{\mathrm{\Phi }}_j-\frac{1}{2}\sqrt{g}V(x^i){\mathrm{\Phi }}^2$, where $g$ is the metric of an arbitrary space. Our approach is based on a connection between the conformal Killing group associated with $g$ and the Noether symmetries of $L(x^i,\mathrm{\Phi },{\mathrm{\Phi }}_i)$. To this effect, we select certain spaces that are characterized by a nonzero Weyl tensor.

In this paper, we examine the viability of Bianchi type V universe in $f(R,T)$ theory of gravitation. To solve the field equations, we have considered the power law for scale factor and constructed a singular Lagrangian model which is based on the coupling between Ricci scalar $R$ and trace of energy–momentum tensor $T$. We find the constraints on Hubble constant $H_0$ and free parameter $n$ with 46 observational Hubble dataset and obtain pretty satisfactory results. The physical features of the model and transitional behavior of equation of state (EOS) parameter are analyzed. We examine the nature of physical parameters and validity of energy conditions as well as stability condition. We also present the Om$(z)$ and statefinder diagnostic analysis for the derived model.