Starting from divisibility problem for Fibonacci numbers, we introduce Fibonacci divisors, related hierarchy of Golden derivatives in powers of the Golden Ratio and develop corresponding quantum calculus. By this calculus, the infinite hierarchy of Golden quantum oscillators with integer spectrum determined by Fibonacci divisors, the hierarchy of Golden coherent states and related Fock–Bargman representations

The aim of this paper is to introduce and justify a possible generalization of the classic Bach field equations on a four-dimensional smooth manifold M in the presence of field φ, given by a smooth map with source M and target another Riemannian manifold. Those equations are characterized by the vanishing of a two times covariant, symmetric, traceless and conformally invariant tensor field, called

The one-variable q-coherent states attached to the q-disc algebra are constructed and used to obtain the q-Bargmann–Fock realization of its Fock representation. Then, this realization is used to obtain the q−1-continuous Hermite polynomials as well as continuous and discrete q-Hermite polynomials by using a pair of Hermitian canonical conjugate operators and two pairs of the non-Hermitian conjugate

In this note, we characterize 1+n doubly twisted spacetimes in terms of “doubly torqued” vector fields. They extend Bang–Yen Chen’s characterization of twisted and generalized Robertson–Walker spacetimes with torqued and concircular vector fields. The result is a simple classification of 1+n doubly-twisted, doubly-warped, twisted and generalized Robertson–Walker spacetimes.

In this paper, in terms of taking values in a commutative subalgebra Zn of Lie algebra gl(n,ℂ), one establishes two novel extended Zn-Heisenberg ferromagnet models in both (1+1) and (2+1)-dimensions and derives their corresponding Lax representations. Moreover, we present their geometrical equivalent equations which are Zn-nonlinear Schrödinger equations.

We propose a simple analytical model for Harmonic oscillator potential that is associated to the generalized uncertainty principle (GUP) in the presence of energy-dependent mass. A formal condition connected with these systems is based on the mathematical structure of modified quantum mechanics. Consequently, thanks to Feynman’s path integrals formalism, we are able to treat the reorganization of wave

Implications of the Raychaudhuri equation in focusing of geodesic congruences are studied in the framework of scalar–tensor theory of gravity. Specifically, we investigate the Brans–Dicke theory and Bekenstein’s scalar field theory. In both of these theories, we deal with a static spherically symmetric distribution and a spatially homogeneous and isotropic cosmological model as specific examples. We

We construct a new class of d-dimensional black hole solutions with Toroidal horizons in f(R) gravity framework which is surrounded by quintessence and string cloud configuration, whose asymptotic structures are determined by the quintessential state parameter ωq and dimension’s parameter d. We point out that the asymptotic behavior of the obtained solutions is neither asymptotically flat nor (A)dS

In this paper, we construct a new approach of spherical magnetic Lorentz flux of spherical 𝕊α-magnetic flows of particles by the spherical frame in 𝕊2 spherical space. Eventually, we obtain some optical conditions of spherical 𝕊α-magnetic Lorentz flux by using directional spherical fields. Moreover, we determine spherical magnetic Lorentz flux for spherical vector fields. Also, we give new construction

In this paper, we consider homothetic Killing vectors in the class of stationary axisymmetric vacuum (SAV) spacetimes, where the components of the vectors are functions of the time and radial coordinates. In this case, the component of any homothetic Killing vector along the z direction must be constant. First, it is shown that either the component along the radial direction is constant or we have

We consider the usual Einstein–Hilbert action in a Metric-Affine setup and in the presence of a Perfect Hyperfluid. In order to decode the role of shear hypermomentum, we impose vanishing spin and dilation parts on the sources and allow only for non-vanishing shear. We then consider an FLRW background and derive the generalized Friedmann equations in the presence of shear hypermomentum. By providing

This paper looks at how changes of coordinates on a pseudo-Riemannian manifold induce homogeneous linear transformations on its tangent spaces. We see that a pseudo-orthonormal frame in a given tangent space is the basis for a set of Riemann normal coordinates. A Lorentz subgroup of the general linear transformations preserves this pseudo-orthonormality. We borrow techniques from the methodology of

In this paper, we will show that a power law asymptotic de Sitter inflation will be established for all values of Hankel indices ν that relate to the different background spacetimes of the universe in their evolution. First, we calculate the relations for the Hubble, deceleration, slow roll and the equation of state parameters in terms of the Hankel function index ν. We then show that the obtained

This paper derives the elements of classical Einstein–Cartan theory (EC) from classical general relativity (GR) in two ways. (I) Derive discrete versions of torsion (translational holonomy) and the spin-torsion field equation of EC from one Kerr solution in GR. (II) Derive the field equations of EC as the continuum limit of a distribution of many Kerr masses in classical GR. The convergence computations

We give a short review on the status of research on the theoretical foundations of f(𝕋) gravity theories. We discuss recent results on perturbative and non-perturbative approaches, causality and degrees of freedom, and discuss future directions to follow.

In this work, we consider gravitationally induced particle creation scenario to discuss the validity of thermodynamic laws in the context of cubic gravity which is based on an invariant term and constructed from cubic contraction of the Riemann tensor. We consider spatially flat FRW universe filled with a perfect fluid assuming an equation of state p=(γ−1)ρ with 23≤γ≤2. By taking the Hubble horizon

A general theory of dynamics is formulated with the aim of its application in emergent quantum mechanics. In such a framework, it is argued that the fundamental dynamics of emergent quantum mechanics must be non-reversible.

In this paper, model of charged gravastar under f(T) modified gravity is obtained. The model has been explored by taking the diagonal tetrad field of static spacetime together with electric charge. To solve the Einstein–Maxwell field equations, along with f(T) gravity, we assume the existence of a conformal Killing vector which relates between geometry and matter through the Einstein–Maxwell field

Cosmological models with an inhomogeneous viscous dark fluid, coupled with dark matter in the Friedmann–Robertson–Walker (FRW) flat universe, are considered. The influence of thermal effects caused by Hawking radiation on the visible horizon is studied, in connection with the classified Types I and III singularities which are known to occur within a finite amount of time. Allowance of thermal effects

We construct a space of quantum states and an algebra of quantum observables, over the set of all metrics of arbitrary but fixed signature, defined on a manifold. The construction is diffeomorphism invariant, and unique up to natural isomorphisms.

A few questions related to white dwarfs’ physics is posed. It seems that the modified gravity framework can be a good starting point to provide alternative explanations to cooling processes, their age determination, and Chandrasekhar mass limits. Moreover, we have also obtained the Chandrasekhar limit coming from Palatini f(ℛ) gravity provided by a simple Lane–Emden model.

In this paper, for the study of integrability, symmetry analysis, group invariant solutions and conservation laws, the Mikhailov–Novikov–Wang equation is considered. Firstly, Painlevé analysis is being employed to study the integrability properties for the considered equation so as to check the possibility that this equation passes the Painlevé test. Secondly, Lie group analysis is studied for finding

In this paper, a well-behaved new model of anisotropic compact star in (3+1)-dimensional spacetime has been investigated in the background of Einstein’s general theory of relativity. The model has been developed by choosing grr component as Krori–Barua (KB) ansatz [Krori and Barua in J. Phys. A, Math. Gen.8 (1975) 508]. The field equations have been solved by a proper choice of the anisotropy factor

In this study, Friedmann–Robertson–Walker space-time filled with a perfect fluid in f(R,T) modified theory, where R is the Ricci scalar and T is the trace of the energy–momentum tensor of matter, has been considered. The investigation of the phase transition of the universe from the decelerating expansion phase to the accelerating one has been made by adopting a special form of the varying deceleration

In this study, we discuss a relationship between the behavior of nonlinear dynamical systems and geometry of a system of second-order differential equations based on the Jacobi stability analysis. We consider how a maximal Lyapunov exponent is related to the geometric quantities. As a result of a theoretical investigation, the maximal Lyapunov exponent can be represented by a nonlinear connection and

This work is focused on the study of charged wormholes in the following two aspects: (i) to obtain exotic matter free effective charged wormhole solutions and (ii) to determine deflection angle for gravitational lensing effect. We have defined a novel redshift function, obtained wormhole solutions using the background of f(R) theory of gravity and found the regions obeying the weak energy condition

In this paper, we give some constructions for the applications of optical magnetic Heisenberg spherical ferromagnetic chain of T - timelike magnetic particle by spherical de Sitter frame in de Sitter space. This aim may be concluded by well-known de Sitter frame or a new alternative spherical frame with an optical magnetic spherical Heisenberg ferromagnetic chain. Moreover, we achieve total magnetic

In this paper, we have introduced a novel integral transform namely linear canonical curvelet transform (LCCT). Firstly, we established basic properties of LCCT including admissibility condition, Moyals principle, inversion formula and range theorem. Toward the culmination of the paper, we formulate a couple of Heisenberg-type inequalities associated with LCCT.

We clarify and discuss a misunderstanding between uniform completeness and metric completeness that has appeared in the literature in a study on the Alexandrov topology for a spacetime.

We prove the existence and uniqueness of Levi-Civita connections for strongly σ-compatible pseudo-Riemannian metrics on tame differential calculi. Such pseudo-Riemannian metrics properly contain the classes of bilinear metrics as well as their conformal deformations. This extends the previous results in [J. Bhowmick, D. Goswami and S. Mukhopadhyay, Levi-Civita connections for a class of spectral triples

In this paper, we examine the functional forms of the potentials W(u,v,xA) that emerge from the Lagrangian of the pp-wave spacetime. To facilitate this investigation, Noether symmetries are employed as well as their linear combinations and subalgebras. We exploit the geometric fact that Noether point symmetries of geodesic Lagrangians are generated from the Homothetic algebra of spacetimes. Thus, we

The aim of this paper is to find conformal vector fields (CVFs) for some vacuum classes of the pp-waves space-times in the ghost free infinite derivative gravity (IDG). In order to find the CVFs of the above-mentioned space-times in the IDG, first, we deduce various classes of solutions by employing a classification procedure that in turn leads towards 10 cases. By reviewing each case thoroughly by

Given the class of Finsler spaces with Lorentzian signature (M,L) on a manifold M endowed with a timelike vector field 𝒳 satisfying g(x,y)(𝒳,𝒳)<0 at any point (x,y) of the slit tangent bundle, a pseudo-Riemannian metric defined on M of signature n−1 is associated to the fundamental tensor g. Furthermore, an affine, torsion free connection is associated to the Chern connection determined by L. The

In this paper, we examine massless scalar field by using unimodular f(R) theory. It is taken into account unimodular and cylindrically symmetric spacetime which provides convenience in researching black hole. The field equations in unimodular f(R) theory for given spacetime with massless scalar field and additional Bianchi identities are solved. Cylindrically symmetric anti-de Sitter (AdS)–Schwarzschild-like

The aim of this paper is to obtain some results for quotion Yamabe solitons with concurrent vector fields. We prove quotion Yamabe soliton (Mn,g,vT,λ) on a hypersurface in Euclidean space ℝn+1 contained either in a hyperplane or in a sphere 𝕊n.

We study statistical submersions between statistical manifolds. In particular, we establish Chen–Ricci inequalities of statistical submersions between statistical manifolds and a δ(2,2) Chen-type inequality for statistical submersions. Some applications are also given.

F(R) theory of gravity is claimed to admit a host of conserved currents under the imposition of Noether symmetry following various techniques. However, for a constrained system such as gravity, Noether symmetry is not on-shell. As a result, the symmetries do not necessarily satisfy the field equations in general, constraints in particular, unless the generator is modified to incorporate the constraints

f(Q,T) gravity is a recently proposed modified theory of gravity due to Xu et al. (2019). It is an extension of the symmetric teleparallel gravity, in which the gravitational action is given by an arbitrary function f(Q,T) of the non-metricity tensor Q and the trace of energy-momentum tensor T. In this paper also, we have investigated the cosmological model with Friedmann–Lemaitre–Robertson–walker

We determine and describe all the Ricci solitons within a very large class of Siklos metrics. As an application, the Ricci soliton equation is completely solved for several classes of Siklos metrics admitting additional Killing vector fields (in particular, for several homogeneous ones).

The continuously decreasing curvature of spacetime has been proposed to be due to the phenomenon like Hawking radiation, the collapse of black holes and neutron stars. It has been found that during these phenomena, energy of source (black hole and neutron stars) decreases. In this paper, we explore this loss in energy of the source by introducing a time conformal factor in the corresponding spacetime

In this paper, warped product in Hermitian and Kählerian manifolds was considered, and almost complex structure on the warped product is defined. Also, warped product almost Hermitian manifolds were defined. According to the holomorphic sectional curvature of Kählerian manifolds, the Einstein condition for constructed warped product Kählerian manifolds is obtained.

Due to the extra degrees of freedom, special affine Fourier transform (SAFT) has achieved a respectable status within a short span and got versatile applicability in the areas of signal processing, image processing, sampling theory, quantum mechanics. However, due to its global kernel, SAFT fails to obtain local information of non-transient signals. To overcome this, in this paper, we introduce the

A new U(1)-invariant nonlocal coupled nonlinear Schrödinger type system consists of a real scalar and two different complex variables as well as its equivalent imaginary quaternionic–complex version is obtained from geometric non-stretching curve flows in the quaternionic–Kähler symmetric space G2/SO(4). The derivation uses Hasimoto variables imposed by a parallel moving frame along the curve. The

Discrete Euler–Lagrange equations are studied over double cross product Lie groupoids. As such, a geometric framework for the local analysis of a discrete dynamical system is established. The arguments are elucidated on the local discrete dynamics of a gauge groupoid. The discrete Elroy’s beanie is studied as a physical example.

Different canonical formalisms for higher order theories lead to different phase-space structures of the Hamiltonian. Canonical equivalence of these Hamiltonians at the classical level does not assure the same in the quantum domain, due to nonlinearity. It has been proved in the isotropic models, that the “Dirac constraint analysis” (after taking care of divergent terms) and “Modified Horowitz Formalism”

We show that the matter Lagrangian of an ideal fluid equals (up to a sign depending on its definition and on the chosen signature of the metric) the total energy density of the fluid, i.e. rest energy density plus internal energy density.

The purpose of this work is to present stellar models for anisotropic matter distribution in the framework of f(T) gravity with torsion scalar T. In this regard, we use the interior geometry of Tolman–Kuchowicz spacetime having the potential components of the form ψ=Br2+2lnC and χ=ln(1+ar2+br4), where a, b, B and C are constants which have been evaluated with the aid of matching conditions on the surface

In this paper, we present a new geometric interpretation of the notion of the Heisenberg antiferromagnetic spin for quasi flows of normal magnetic particles with quasi frame in 3D space. Moreover, we investigate integrability conditions for quasi new frame fields. Therefore, we determine necessary and sufficient condition for given normal magnetic particles with flow in space. Additionally, we present

The main purpose of this paper is to investigate LRS Bianchi type I metric in the presence of perfect fluid and dark energy. In order to obtain a deterministic solution of the field equations we have assumed that the two sources of the perfect fluid and dark energy interact minimally with separate conservation of their energy–momentum tensors as well EoS parameter of the perfect fluid is assumed to

The explicit form of the field equations has been obtained by varying the action of the four-dimensional Einstein-dilaton gravity in the presence of the scalar-coupled exponential nonlinear electrodynamics. The exact black hole solutions of the field equations have been obtained in an energy-dependent spherically symmetric geometry. It has been found that the solution of the scalar field equation can

In this work, a new form of the logarithmic shape function is proposed for the linear f(R,T) gravity, f(R,T)=R+2λT where λ is an arbitrary coupling constant, in wormhole geometry. The desired logarithmic shape function accomplishes all necessary conditions for a traversable and asymptotically flat wormhole. The obtained wormhole solutions are analyzed from the energy conditions for different values

We consider the notion of cosmological symmetry, i.e. spatial homogeneity and isotropy, in the field of teleparallel gravity and geometry, and provide a complete classification of all homogeneous and isotropic teleparallel geometries. We explicitly construct these geometries by independently employing three different methods, and prove that all of them lead to the same class of geometries. Further

In this paper, we first study the applications of the wave propagation flow in the normal direction, which is assumed to be the path of the propagated light radiated by Heisenberg ferromagnetic equation. Then the Coriolis phase is mainly used to demonstrate the relationship between the geometric magnetic phase and parallel transportation of the wave propagation field of the evolving light radiating

We discuss the advantages of using metric theories of gravity with curvature–matter couplings in order to construct a relativistic generalization of the simplest version of Modified Newtonian Dynamics (MOND), where Tully–Fisher scalings are valid for a wide variety of astrophysical objects. We show that these proposals are valid at the weakest perturbation order for trajectories of massive and massless

In this paper, geometries and supergeometries are analyzed from the point of view of the coset coherent states. To this end, before detailing the different factorizations of the simplest cosets, the dynamics and structure of Supercoherent states of the Klauder–Perelomov type (that are defined taking into account the geometry of the coset based on the simplest supergroup SU(2|1) in the context of extensions

We consider a new model which consists of a DNA together with a RNA. Here, we assume that DNA is from a mammal or bird but RNA comes from a virus. To study thermodynamic properties of this model, we use methods of statistical mechanics, namely, the theory of Gibbs measures. We use these measures to describe phases (states) of the DNA–RNA system. Using a Markov chain (corresponding to Gibbs measure)

Using the fact that neutrinos only participate in weak and gravitational interactions, we explore the possibility of having their masses emerged at the intersection between extended electroweak theory and theory of gravity. We describe how these two seemingly incompatible theories could be embedded in a lepton-number violating 5-dimensional Lagrangian ℒ5. A peculiar feature of this approach is its

We consider Eigen-functions of the Laplace–Beltrami Operator on n-Spheres and characterize them in terms of their local plane wave behavior. We estimate the local spectrum of wave numbers by approximating the Spherical harmonics in the locally flat neighborhood around a point on the Spheres. These local wave numbers are shown to obey an interesting Pythagorean type relation. Based on this relation

We study slant submersions and conformal slant submersions from nearly Kaehler manifolds onto Riemannian manifolds and investigate conditions for such maps to be totally geodesic maps. We also obtain conditions for a slant submersion and a conformal slant submersion from a nearly Kaehler manifold onto a Riemannian manifold to be a harmonic map and a harmonic morphism, respectively.

This paper deals with the violation or retention of symmetries associated with the self-adjoint extension of the Hamiltonian for homogeneous but anisotropic Bianchi I cosmological model. This extension is required to make sure the quantum evolution is unitary. It is found that the scale invariance is lost, but the Noether symmetries are preserved.