Rip cosmological models have been investigated in the framework of f(T,𝒯) theory of gravity, where T denotes the torsion and 𝒯 is the trace of the energy–momentum tensor. These phantom cosmological models revealed that at initial epoch a EoS parameter ω<−1 tends asymptotically at late phase to −1(ω→−1). On the other hand, Wormhole Solutions and Big Trip have been subject to an investigation. The

In this work, several pinched conditions on the Laplacian and gradient of the warping function are found in consideration of warped product submanifolds structure that force to homology groups vanish with no stable currents. Also, it is proved that a warped product pointwise semi-slant submanifold Mn that is compact and oriented in an odd-dimensional spheres 𝕊2(p2+q)+1 and 𝕊2(p+q)+1, has no stable

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

In this paper, we have presented the Einstein–Maxwell equations which are described by the spherically symmetric spacetime in the presence of charge by exploiting the Tolman–Kuchowicz spacetime. The corresponding field equations are constructed and the form of charge distribution is chosen to be Q0(r)=Q(rR)3=ξr3, where ξ is a constant quantity. We also find the values of unknown constants from junction

We reconstruct the Cartan Equations of null Killing magnetic curve γ(s) in ℝ13 with Killing magnetic vector field V under the new Cartan frame {γ′(s),V∧γ′(s),V′∧γ′(s)−V}, which describe some new geometrical properties of γ(s). The singularity properties of the rectifying surfaces and the binormal osculating surfaces of null Killing magnetic curves are given. As an application, two examples are given

In this work, the Dirac equation is studied in the z=0 Lifshitz black hole (Z0LBH) spacetime. The set of equations representing the Dirac equation in the Newman–Penrose (NP) formalism is decoupled into a radial set and an angular set. The separation constant is obtained with the aid of the spin weighted spheroidal harmonics. The radial set of equations, which are independent of mass, is reduced to

We construct the q-deformed fuzzy Dirac and chirality operators on quantum fuzzy Podles sphere Sqμ2. We will show that there are a class of these operators on Sqμ2 in which all of them in the limit case q→1 has the correct fuzzy sphere limit as well as they have correct commutative limit in the limit case when q→1 and noncommutative parameter l tends to infinity.

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.

We geometrically examine the entanglement in symmetric multiquibt states using the spin coherent states properties. We employ the Majorana representation to examine how coherent (polarized) and unpolarized states can be represented in the Bloch sphere and subsequently to quantify entanglement in multipartite systems. Entanglement can be viewed as a distance separate two points in Bloch sphere and how

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

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

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 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.

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 studied the cosmological implications of generalized ghost Tsallis holographic dark energy in the framework of Randall–Sundrum II braneworld and Chern–Simons modified gravity in flat FRW universe. We discuss the cosmological parameters like equation of state parameter, deceleration parameter, squared speed of sound, Om-diagnostic and planes like evolving equation of state parameter

In this short note, we will prove in a few steps that the new tetrads introduced previously in Einstein–Maxwell four-dimensional Lorentzian spacetimes, where gravitational and non-null electromagnetic fields are present, contain both the necessary information to provide the gravitational field and the necessary information to provide the electromagnetic field as well. These new tools thus become grand

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

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 paper, we study naturally reductive (α,β)-metrics on homogeneous manifolds. We show that naturally reductive (α,β)-metrics arise only when α is naturally reductive and some conditions on ϕ is satisfied. We give an explicit formula for the flag curvature of naturally reductive (α,β)−metrics which improves the flag curvature formula of naturally reductive Randers metrics given in [D. Latifi,

The focus of this paper is on Kawahara equation(KE) which models diverse variety of waves enforced in many branches of applied sciences. Symmetries to the considered equation are successfully obtained by practicing nonclassical method. According to nonclassical symmetries, KE has been reduced to numerous ODEs. Further, these ODEs are treated such that new analytic solutions are determined by applying

We show how to lift a Riemannian metric and almost symplectic form on a manifold to a Riemannian structure on a canonically associated supermanifold known as the antitangent or shifted tangent bundle. We view this construction as a generalization of Sasaki’s construction of a Riemannian metric on the tangent bundle of a Riemannian manifold.

The propagation of cylindrical shock wave under the influence of axial magnetic field in rotating medium under isothermal flow condition is investigated. The density, magnetic field and azimuthal and axial components of fluid velocity are assumed to be varying in the undisturbed medium. The arbitrary constants appearing in the expressions for infinitesimals of the Local Lie group of transformations

We introduce almost contact and cosymplectic Finsler manifolds. Then, we characterize almost contact Randers metrics. It is proved that a cosymplectic Finsler manifold of constant flag curvature must have vanishing flag curvature. We prove that every cosymplectic Finsler manifold is a Landsberg space, under a mild condition. Finally, we show that a cosymplectic Finsler manifold is a Douglas space if

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

Using the methods of ordinary quantum mechanics, we study κ-Minkowski space as a quantum space described by noncommuting self-adjoint operators, following and enlarging T. Poulain and J.-C. Wallet, “κ-Poincaré invariant orientable field theories with at 1-loop: Scale-invariant couplings, preprint (2018), arXiv:1808.00350 [hep-th]. We see how the role of Fourier transforms is played in this case by

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 paper, we classify all simply connected five-dimensional nilpotent Lie groups which admit (α,β)-metrics of Berwald and Douglas type defined by a left invariant Riemannian metric and a left invariant vector field. During this classification, we give the geodesic vectors, Levi-Civita connection, curvature tensor, sectional curvature and S-curvature.

In this paper, Bianchi type I space-times in the f(R) theory of gravity are classified via conformal vector fields using algebraic and direct integration techniques. In this classification, we show that the conformal vector fields are of dimension four, five, six or fifteen. Additionally, we found that non-conformally flat Bianchi type I space-times admit conformal vector fields of dimension four,

We characterize the second variation of an higher order Lagrangian by a Jacobi morphism and by currents strictly related to the geometric structure of the variational problem. We discuss the relation between the Jacobi morphism and the Hessian at an arbitrary order. Furthermore, we prove that a pair of Jacobi fields always generates a (weakly) conserved current. An explicit example is provided for

We investigate the chameleon Brans–Dicke gravity with new holographic dark energy which includes a non-minimal coupling between matter and scalar field. We use parameterized forms of deceleration parameter for flat FRW universe, which play a vital role to describe the nature of cosmic acceleration. We explore the cosmological parameters like Hubble parameter, equation of state parameter as well as

Assuming the most general form of static spherically symmetric space-times, we search for the conformal vector fields in f(R, G) gravity by means of algebraic and direct integration approaches. In this study, there exist six cases which on account of further study yield conformal vector fields of dimension four, six and fifteen. During this study, we also recovered some well-known static spherically

In this paper, we study non-integrable distributions in a Riemannian manifold with a semi-symmetric metric connection, a kind of semi-symmetric non-metric connection and a statistical connection. We obtain the Gauss, Codazzi, and Ricci equations for non-integrable distributions with respect to the semi-symmetric metric connection, the semi-symmetric non-metric connection and the statistical connection

We consider the possibility to enlarge the class of symmetries realized in standard local field theories by introducing infinite order derivative operators in the actions, which become nonlocal. In particular, we focus on the Galilean shift symmetry and its generalization in nonlocal (infinite derivative) field theories. First, we construct a nonlocal Galilean model which may be UV finite, showing

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

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

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

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. B781 (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

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

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

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

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

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 (κ,μ)′-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≥1. Such surfaces, that we call S2(N), have positive constant Gaussian curvature, K, but are spheres only when N=1. They have edges, and, for any fixed K, have maximal

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+β2βt+k, which is time-dependent (here, k and β are arbitrary constants)

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

In this study, we investigate the potential functions V(xi) that appear in the Lagrangian L(xi,Φ,Φi)=12ggijΦiΦj−12gV(xi)Φ2, 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(xi,Φ,Φi). 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 H0 and free parameter n with 46 observational

This is a review of recent results regarding the application of Connes’ noncommutative geometry to the Standard Model, and beyond. By twisting (in the sense of Connes-Moscovici) the spectral triple of the Standard Model, one does not only get an extra scalar field which stabilises the electroweak vacuum, but also an unexpected 1-form field. By computing the fermionic action, we show how this field

We review recent results obtained by using the spectral action applied to some simple physical models built in the noncommutative geometry framework. The first result, based on the generalization of the spectral action principle to the case of the fermionic action leads to the lowest order corrections that can possibly explain the huge difference between the electron and neutrino masses. In the second

A sharper formulation is presented for an interpretation of quantum mechanics advocated by the author. We claim that only those quantum theories should be considered for which an ontological basis can be constructed. In terms of this basis, the entire theory can be considered as being deterministic. An example is illustrated: massless, noninteracting fermions are ontological. Subsequently, as an essential

Hawking temperature for a large class of black holes (Schwarzschild, Reissner–Nordström, (Anti) de Sitter, with spherical, toroidal and hyperboloidal topologies) is computed using only laws of classical physics plus the “classical” Heisenberg Uncertainty Principle. This principle is shown to be fully sufficient to get the result, and there is no need to this scope of a Generalized Uncertainty Principle

A brief review of our previously introduced forward and backward in time formalism for non-relativistic electron diffraction and its relativistic extension to study photons in time and space is presented. The zero-point energy in the Planck black body spectrum emerges naturally once time-symmetric motion — inherent in Maxwell equations — is invoked for photons. A study of two-slit experiments for slits

We derive a sufficient condition for the existence of the entropy current of a fluid at local thermodynamic equilibrium using relativistic quantum statistical mechanics, and put forward a general method to calculate it. We also work out a specific calculation in a non-trivial case of interest, namely a system at global thermodynamic equilibrium with proper acceleration of constant magnitude along the

I review here some motivations to consider a theory of gravity based on independent metric and connection, and its status as a quantum theory.

The study of the damped harmonic oscillator shows that dissipation could be seen at the origin of the zero point energy, which is the signature of quantum behavior. This is in accord with ’t Hooft proposal that loss of information in a completely deterministic dynamics would play a rôle in the quantum mechanical nature of our world. We show the equivalence, within quite general conditions, between

We consider a functional relation between a given Wilsonian renormalization group (RG) flow, which has to be related to a specific coarse-graining procedure, and an infinite family of (UV cutoff) scale-dependent field redefinitions. Within this framework, one can define a family of Wilsonian proper-time (PT) exact RG equations associated to an arbitrary regulator function. New applications of these