The Noether–Bessel-Hagen theorem can be considered a natural extension of Noether Theorem to search for symmetries. Here, we develop the approach for dynamical systems introducing the basic foundations of the method. Specifically, we establish the Noether–Bessel-Hagen analysis of mechanical systems where external forces are present. In the second part of the paper, the approach is adopted to select

In this paper, we investigate the charged static spherically symmetric models in f(R) theory of gravity. We consider a linear equation of state (EoS) in the background of anisotropic matter configuration. We formulate the modified field equations and implement Durgapal transformation to examine the gravitational nature of compact stellar objects. For this purpose, we choose a specific gravitational

We define a functional 𝒥(h) for the space of Hermitian metrics on an arbitrary Higgs bundle over a compact Kähler manifold, as a natural generalization of the mean curvature energy functional of Kobayashi for holomorphic vector bundles, and study some of its basic properties. We show that 𝒥(h) is bounded from below by a nonnegative constant depending on invariants of the Higgs bundle and the Kähler

We consider the sets of Dirac–Maxwell and Rarita–Schwinger–Maxwell equations in ℝ×S3 spacetime. Using the Hopf coordinates, we show that these equations allow separation of variables and obtain the corresponding analytic and numerical solutions. It is also demonstrated that the current of the Dirac field is related to the Hopf invariant on the S3→S2 fibration.

In this paper, we investigate the topology of a wormhole from the viewpoint of the theory of retracting and var-folding. We deduce the equatorial geodesics on the line element of the wormhole and discuss the minimum deformation retract related to this space. Using the Lagrangian equations we find that there is a type of minimum retraction of a wormhole with associated topology. We also extend the result

In this paper, we introduce the notion of Koszul–Vinberg–Nijenhuis (KVN) structures on a left-symmetric algebroid as analogues of Poisson–Nijenhuis structures on a Lie algebroid, and show that a KVN-structure gives rise to a hierarchy of Koszul–Vinberg structures. We introduce the notions of KVΩ-structures, pseudo-Hessian–Nijenhuis structures and complementary symmetric 2-tensors for Koszul–Vinberg

We present a systematic treatment of line bundle geometry and Jacobi manifolds with an application to geometric mechanics that has not been noted in the literature. We precisely identify categories that generalize the ordinary categories of smooth manifolds and vector bundles to account for a lack of choice of a preferred unit, which in standard differential geometry is always given by the global constant

Geometrical approach to continuum mechanics allowing an atomistic treatment is developed. It suggests a body as a surface immersed into ambient space. Four kinds of surfaces inherent to basic deformations determine classical dynamics of the atoms alongside their spatial coordinates. For uniaxial stretch, this surface is isomorphic to the cylinder. For a simple shear, it is the twisted cylinder, for

The equation for fluid flow in porous media is analyzed in this paper with the aid of Lie symmetry method (LSM) and invariant subspace method (ISM). Infinitesimal generators, the entire geometric fields of the vectors and the symmetry groups of the equation being considered are given. One-dimensional optimal systems of sub-algebra are reported with corresponding reduced nonlinear ordinary differential

In this paper, we introduce the cohomology theory of relative Rota–Baxter operators on Leibniz algebras. We use the cohomological approach to study linear and formal deformations of relative Rota–Baxter operators. In particular, the notion of Nijenhuis elements is introduced to characterize trivial linear deformations. Formal deformations and extendibility of order n deformations of a relative Rota–Baxter

In this paper, we find exact string cosmological solutions for FRW cosmology, by using the Hojman symmetry approach. The string cosmology under consideration includes a scalar field ψ(t) with the potential W(ψ), and a totally antisymmetric field strength Hμνρ which is specifically defined in terms of the scale factor a(t). We show that for this string cosmology, Hojman conserved quantities exist using

This paper deals with the Newton–Wigner position observable for Poincaré-invariant classical systems. We prove an existence and uniqueness theorem for elementary systems that parallels the well-known Newton–Wigner theorem in the quantum context. We also discuss and justify the geometric interpretation of the Newton–Wigner position as “center of spin”, already proposed by Fleming in 1965 again in the

If a three-dimensional N(k)-contact metric manifold M admits a Yamabe soliton of type (M,g,V), then the manifold has a constant scalar curvature and the flow vector field V is Killing. Furthermore, either M has a constant curvature k or the flow vector field V is a strict contact infinitesimal transformation. Also, we prove that if the metric of a three-dimensional N(k)-contact metric manifold M admits

We analyze the interaction of the induced electric dipole moment of a neutral particle with an electric field in elastic medium with a charged disclination from a semiclassical point of view. We show that the interaction of the induced electric dipole moment of a neutral particle with an electric field can yield an attractive inverse-square potential, where it is influenced by the topology of the disclination

In this paper, we have presented a cosmological model where a phantom scalar field is minimally coupled to dark matter component. Noether symmetry method was applied both to investigate the cosmological solution and to find out what is the form of the potential of scalar field and the unknown function in the considered model. By using this method, these forms are resulted as trigonometric functions

We describe a simple approach for a possible connection between the exterior and interior of black-holes. According to our result, the Schwarzschild radius determines a 2-dimensional sphere that separates two worlds: the exterior, where ordinary matter moves with velocities less than the light velocity, and the interior, where tachyons move with velocities greater than the light velocity. Moreover

We consider the motion planning of an object in a Riemannian manifold where the object is steered from an initial point to a final point utilizing optimal control. Considering Pontryagin Minimization Principle we compute the Optimal Controls needed for steering the object from initial to final point. The Optimal Controls were solved with respect to time t and shown to have norm 1 which should be the

In this paper, we analyze the weak gravitational lensing in the context of Einstein-nonlinear-Maxwell–Yukawa black hole. To this desire, we derive the deflection angle of light by Einstein-nonlinear-Maxwell–Yukawa black hole using the Gibbons and Werner method. For this purpose, we obtain the Gaussian curvature and apply the Gauss–Bonnet theorem to find the deflection angle of Einstein-nonlinear-Maxwell–Yukawa

All classes of spatially homogeneous spacetime models in the generalized scalar–tensor theory of gravitation are found to allow the integration of the equations of motion of test particles and the eikonal equation by the method of separation of variables by type (3.1). Three classes of exact solutions are obtained that relate to Shapovalov wave-like spacetime models. The resulting spacetime models

In this work, LRS Bianchi type-I cosmological model with 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 proposing a new special form of time-varying deceleration parameter in terms of Hubble parameter, the

In this paper, we show that a Finsler warped product metric is of almost vanishing H-curvature if and only if it is of almost vanishing χ-curvature. Furthermore, the corresponding one form is exact.

In this paper, we will concentrate on a systematic investigation of finding Lie point symmetries of the nonlinear (2+1)-dimensional time-fractional Kramers equation via Riemann–Liouville and Caputo derivatives. By using the Lie group analysis method, the invariance properties and the symmetry reductions of the time-fractional Kramers equation are provided. It is shown that by using one of the symmetries

In this paper, we study the thermodynamics of short-range central potentials, namely, the Lee–Wick (LW) potential, and the Plasma potential. In the first part of the paper, we obtain the numerical solution for the orbits equation for these potentials. Posteriorly, we introduce the thermodynamics through the microcanonical and canonical ensembles formalism defined on the phase space of the system. We

Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel σ-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations. Considering the geometric formulation of quantum mechanics we give a description of quantum propositions in terms of fuzzy events in a complex projective space equipped with Kähler

An interest problem arises to determine the surfaces in the Euclidean three space, which admit at least one nontrivial isometry that preserves the principal curvatures. This leads to a class of surface known as a Bonnet surface. The intention of this study is to examine a Bonnet ruled surface in dual space and to calculate the dual geodesic trihedron of the dual curve associated with the Bonnet ruled

We propose a new unified model that describes dark energy and dark matter in the context of f(R,ϕ) gravity using a massive scalar field in five dimensions. The scalar field is considered in the bulk that surrounds the 3-brane in branworld model. We show that for a specific choice of the f(R,ϕ) function, we can describe the Einstein gravitation in 4-dimensional space-time. We obtain a relationship between

We have studied thermal fluctuations from neutral as well as charged and rotating charged cylindrical black holes. In this context, we computed modified expressions for several thermodynamic quantities such as entropy, mass and heat capacity for all these types of cylindrical black holes. It is shown that these quantities change their forms under the influence of thermal fluctuations. We also discuss

Within F(B2) modified Weyl gravity, we consider a model of a spin-1/2 electric charge consisting of interior and exterior regions. The interior region is determined by quantum gravitational effects whose approximate description is carried out using Weyl gravity nonminimally coupled to a massless Dirac spinor field. The interior region is embedded in exterior Minkowski spacetime, and the joining surface

This study set out to investigate the effect of anisotropy on the ΛCDM model in the framework of Brans−Dicke theory. To this end, astrophysical constraints on this model using current available data including type Ia supernovae (SNIa), the Baryon Acoustic Oscillation (BAO), and the Hubble parameter H(z) data were deployed. Here, we present combined results from these probes, deriving constraints on

In this paper, we obtain the expressions of the ∗-Ricci operator of a three-dimensional almost Kenmotsu manifold M3 and find that the ∗-Ricci tensor is not symmetric for M3. We obtain a necessary and sufficient condition for the ∗-Ricci tensor to be symmetric and proved that if the ∗-Ricci tensor of a non-Kenmotsu almost Kenmotsu 3-h-manifold M3 is symmetric, then M3 is locally isometric to a three-dimensional

In this paper, initially we solve the Einstein field equations (EFEs) for a static spherically (SS) symmetric perfect fluid space-times in the f(T,B) gravity with the aid of some algebraic techniques. The extracted solutions are then utilized in order to get conformal vector fields (CVFs). It is important to mention that the adopted techniques enable us to obtain various classes of space-times with

In this work, we have investigated the cosmological bouncing solution in LRS Bianchi-I space-time in framework of f(R,T) gravity. Our study in this paper is based on the modeling of matter bounce scenario in which the universe starts with a matter-dominated contraction phase and transitions into an ekpyrotic phase. Mathematical simulations have been done in the modified general theory of relativity

The stability of two different bounce scenarios from F(R,𝒢) modified gravity at later times is studied, namely a hyperbolic cosine bounce model and a matter-dominated one. After describing the main characteristics of F(R,𝒢) modified gravity, the two different bounce scenarios stemming from this theory are reconstructed and their stability at late stages is discussed. The stability of the hyperbolic

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

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

For a quantum system whose phase space is the cotangent bundle of a Lie group, like for systems endowed with particular cases of curved geometry, one usually resorts to a description in terms of the irreducible representations of the Lie group, where the role of (non-commutative) phase space variables remains obscure. However, a non-commutative Fourier transform can be defined, intertwining the group

In this work, the solutions of traversable wormholes are investigated inside modified f(R) gravity under non-commutative geometry since matter possesses Lorentzian density distribution of a particle-like gravitation source. To find the exact wormhole solutions, two different shape functions b(r)=r0(arar0), 0

This paper investigates the Noether symmetry approach in modified f(ℛ,φ,χ) theory of gravity, where ℛ is the Ricci scalar, φ is a scalar field and χ is the kinetic energy term. For this purpose, we consider Locally Rotationally Symmetric (LRS) Bianchi Type-I spacetimes. The cosmological solutions are developed through Noether symmetry approach. The determining equations are computed in the context

We investigate phase transitions and critical behaviors of the Kerr–Sen black hole in four dimensions. Computing the involved thermodynamical quantities including the specific heat and using the Ehrenfest scheme, we show that such a black hole undergoes a second-order phase transition. Adopting a new metric form derived from the Gibss free energy scaled by a conformal factor associated with extremal

The purpose of this work is to study the Tsallis, Rényi and Sharma–Mittal holographic dark energy models in order to evaluate the accelerated expansion of the Universe. In this regard, we consider the modified field equations for logarithmic and power law versions of entropy corrected models in FRW Universe filled with interacting dark energy and cold dark matter within the framework of Hořava–Lifshitz

In this paper, we construct Darboux transformations of the noncommutative BKP (ncBKP) hierarchy and the noncommutative CKP (ncCKP) hierarchy. From these Darboux transformations, the explicit differences between the BKP (CKP) hierarchy and the noncommutative BKP (ncCKP) hierarchy can be seen clearly in this paper. These studies might be useful in the M theory and string theory in future.

In this work, we explore the Tsallis holographic dark energy (THDE) model with IR cutoff as Granda–Oliveros horizon describing the Universe experiencing an accelerating expansion phase in the framework of flat Friedmann–Lemaître–Robertson–Walker (FLRW) Universe. The Universe evolution from earlier decelerated to the current accelerated phase is exhibited by the deceleration parameter acquired in the

Within R2 gravity, we study the linear stability of strongly gravitating spherically symmetric configurations supported by a polytropic fluid. All calculations are carried out in the Jordan frame. It is demonstrated that, as in general relativity, the transition from stable to unstable systems occurs at the maximum of the curve mass-central density of the fluid.

The main purpose of this work is to focus on a discussion of Lie symmetries admitted by de Sitter–Schwarzschild spacetime metric, and the corresponding wave or Klein–Gordon equations constructed in the de Sitter–Schwarzschild geometry. The obtained symmetries are classified and the variational (Noether) conservation laws associated with these symmetries via the natural Lagrangians are obtained. In

Quantum and classical physical states are represented in a unified way when they aredescribed by symplectic tomography. Therefore this representation allows us to study directly the necessary conditions for a classical universe to emerge from a quantum state. In a previous work on the de Sitter universe this was done by comparing the classical limit of the quantum tomograms with those resulting from

In this paper, we have investigated the stability of General Relativistic Hydrodynamics (GRHD) model in a Friedmann–Robertson–Walker space-time with the volumetric power law in teleparallel gravity. The basic equations are derived along with its thermodynamical aspects. Thermodynamic temperature and entropy density of the model are also obtained. The state finder diagnostic pair and jerk parameter

In this paper, we study Einstein standard stationary space-times (M,g)=(ℝ×Σ,−βdt2+dt⊗gΣ(ξ,.)+gΣ(ξ,.)⊗dt+gΣ) of dimension n+1≥3 with ξ is conformal on the space-like hypersurface (Σ,gΣ). When Σ is assumed to be connected and complete, we give a criterion so that (M,g) is Einstein. In particular, we show that if (M,g) is Einstein and Σ is complete and connected, then the scalar curvature of M and that

In this paper, we first define a supersymmetric Gelfand–Dickey hierarchy using the Sato equation. Then we introduce some time variables and derivations involving those that from a non-abelian Lie superalgebra. Next, we construct additional symmetries for the supersymmetric Gelfand–Dickey hierarchy with the aid of the Orlov–Schulman operators which involve the above time variables and dressing operators

Coherently with the principle of analogy suggested by Dirac, we describe a general setting for reducing a classical dynamics, and the role of the Noether theorem — connecting symmetries with constants of the motion — within a reduction. This is the first of two papers, and it focuses on the reduction within the Poisson and the symplectic formalism.

In this paper, some analogies between the Shapiro effect in the solar gravitational field and the Sagnac phase shift have been found. Starting from Einstein equivalence principle (EEP), which states the equivalence between the gravitational force and the pseudo-force experienced by an observer in a noninertial frame of reference, we imagine an observer on a rotating platform immersed in a gravitational

In this paper, we investigate some feasible regions for the existence of wormholes by introducing non-commutative geometry in terms of Gaussian and Lorentzian distributions in f(R,G) modified theory of gravity. We explore wormhole solutions by assuming a viable model f(R,G)=f1(R)+f2(G), where f1(R) is assumed to be a linear function of Ricci scalar and f2(G) is chosen to be a power law model. For f(R

We explore the possibility to extend the Heisenberg’s uncertainty principle to a nonlinear extension of the quantum algebra related to a functional operator of the momenta as ℱ(P). We show that such an extension of quantum mechanics is intimately connected to the non-commutative space-time algebra and the Lorentz symmetry deformations. We show that a large class of ℱ(P) models can introduce superluminal

A geometrical construction for a global dynamical time for binary point-like particle systems, modeled by relativistic equations of motions, is presented. Thus, we provide a convenient tool for the calculation of the dynamics of recent models for the dynamics of black holes that use individual proper times. The construction is naturally based on the local Lorentzian geometry of the spacetime considered

In this study, we investigated scalar field in f(G)-gravity by using LRS Bianchi type-I universe. Massless and massive scalar field models are separately constructed in f(G)-gravity. Massless scalar field models are examined in the cases of constant and exponential potential fields. For all models, solutions of field equations are obtained under the consideration of A=Bn. f(G) functions for each model

Here, we have investigated the interaction of Bianchi type-I anisotropic cloud string cosmological model universe with electromagnetic field in the context of general relativity. In this paper, the energy-momentum tensor is assumed to be the sum of the rest energy density and string tension density with an electromagnetic field. To obtain exact solution of Einstein’s field equations, we take the average

In the context of cubic gravity for flat FRW metric we discuss the behavior of cosmological parameters (equation of state (EoS) parameter and square speed of sound) at Hubble horizon with the four different models of Hubble parameter. We observe the validity of generalized second law of thermodynamics (GSLT) and thermal equilibrium condition. It is found that cosmological parameters lie within the

In this paper, we consider the particle on curved graphene space-time. In that case, we calculate the geometric form of potential which is known as Gaussian function. Here, we introduce the metric background which completely corresponds to curved graphene space-times. This metric leads us to obtain the geometry potential and we make the Laplace Beltrami equation in the mentioned metric background.

In this paper, the thermodynamical properties and the phase transitions of the charged accelerating anti-de Sitter (AdS) black holes are investigated in the framework of the f(R) gravity. By studying the conditions for the phase transitions, it has been shown that the P−V criticality and the van der Waals like phase transitions can be achieved for T≈Tc. The Joule–Thomson expansion effects are also

Klein–Gordon oscillator in the background space-time generated by a rotating cosmic string subject to a Cornell-type scalar and Coulomb-type vector potentials including an internal magnetic flux is studied. We obtain the relativistic energy eigenvalues and the corresponding eigenfunctions and analyze a relativistic analogue of the Aharonov–Bohm effect for bound states.

In this paper, we have investigated some cosmological consequences of a quintessence dark energy model. In particular, we have obtained the forms of the equation of state parameter, the deceleration parameter and the field potential by considering a simple relation between the scale factor and the time derivative of the scalar field, instead of assuming any functional form for the scalar field potential