International Journal of Geometric Methods in Modern Physics

We study statistical submersions between statistical manifolds. In particular, we establish Chen–Ricci inequalities of statistical submersions between statistical manifolds and a $\delta (2,2)$ 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. In this paper, we apply the first theorem of Poisson to unveil the fact that not all the conserved currents appearing in the literature for $F(R)$ theory of gravity satisfy the field equations. We also provide a list of available forms of $F(R)$ along with associated conserved currents and construct a generalized action, which might address the cosmic puzzle, elegantly.

$f(Q,T)$ 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 (FLRW) Universe in $f(Q,T)$ theory with $f(Q,T)=\alpha Q^n+\beta T$. Applying the energy conservation condition $\dot{\rho }+3H(\rho +p)=0$, we have obtained the various cosmological parameters viz. Hubble parameter $H(z)$, deceleration parameter $q(z)$, etc. in terms of redshift $z$. Using the available observational Hubble datasets $H(z)$, the best fit values of the model parameters are determined by the $R^2$-test formula. For these obtained values of model parameters, our model represents a transit cosmological model with past decelerating to present accelerating expansion phase of the Universe with the present value $q_0=-0.63$. The point of signature-flipping (transition) is calculated as $z_t=0.469$. We have analyzed the variations of physical parameters viz. matter energy density $\rho$, isotropic pressure $p$, equation of state $\omega =\frac{p}{\rho }$ with respect to redshift $z$ and coupling parameter $\beta$. For checking the viability of our derived model, we have tested energy conditions and also performed statefinder diagnosis. The age of the Universe is also calculated.

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 order to get a nonstatic metric without violating its symmetry structure. This technique gives us information about the loss of momentum and energy of the source. We also consider some novel nonstatic classes of the plane-symmetric spacetime containing 10 Noether symmetries and 7 isometries.

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 concept of novel special affine wavelet transform (NSAWT) and extend key harmonic analysis results to NSAWT analogous to those for the wavelet transform. We first establish some fundamental properties including Moyal’s principle, Inversion formula and the range theorem. Some Heisenberg type inequalities and Pitt’s inequality are established for SAFT and consequently Heisenberg uncertainty principle is derived for NSAWT.

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 $G_2/SO(4)$. The derivation uses Hasimoto variables imposed by a parallel moving frame along the curve. The pseudo-differential bi-Hamiltonian and recursion operators as well as geometric curve evolution from soldering relations of the corresponding curvature and torsion are explicitly computed. The Lax pair for the system is derived by revisiting Drinfeld–Sokolov construction.

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” lead to identical phase-space structure of the Hamiltonian for the gravitational action with curvature squared terms. Here, we extend the same in anisotropic space-time, viz, Bianchi-I, Bianchi-III and Kantowski–Sachs models too. This is a prologue toward canonical quantization.

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 $\psi =B{r}^2+2lnC$ and $\chi =ln(1+a{r}^2+b{r}^4)$, where $a$, $b$, $B$ and $C$ are constants which have been evaluated with the aid of matching conditions on the surface of interior and exterior spacetimes. Off-diagonal tetrad is used to obtain the modified Field Equations (FEs). We use power law of $f(T)$ gravity to get all the physical parameters such as principal stresses, density. We discuss anisotropy of the system and its effects on the system. The physical analysis is also presented by measuring speeds of sound, equilibrium conditions, energy conditions and redshift, etc. We choose some compact star models to present graphical description of the solution.

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 some new constructions for evolution of particle by Heisenberg antiferromagnetic model and we give total magnetic phase for new quasi vector fields in 3D space.

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 be constant. In addition to this we have used a special law of variation of Hubble parameter proposed by Berman that yields constant deceleration parameter. For the two different constant values of deceleration we have obtained two different cosmological models. The physical behaviors of both the models have been discussed by using MATLAB.

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 be obtained by combining two Liouville potentials. We have introduced three types of exponentially charged dilatonic black holes and their thermodynamic properties have been studied noting the effects of rainbow functions. The impacts of rainbow functions on the conserved and thermodynamic quantities of the new black hole solutions have been explored. Through the Smarr mass formula, it has been demonstrated that the first law of black hole thermodynamics remains valid for either of the new rainbow black hole solutions. The quantum gravitational effects on the thermodynamic phase transition or thermal stability of the black holes have been studied by use of the canonical ensemble method. By calculating the black hole heat capacity, the type-1 and type-2 phase transition points and the conditions under which the exponentially charged rainbow black holes are locally stable have been identified.

In this work, a new form of the logarithmic shape function is proposed for the linear $f(R,T)$ gravity, $f(R,T)=R+2\lambda T$ where $\lambda$ 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 of $\lambda$. It has been observed that our proposed shape function for the linear form of $f(R,T)$ gravity, represents the existence of exotic matter and non-exotic matter. Moreover, for $\lambda =0,$ i.e. for the general relativity case, the existence of exotic matter for the wormhole geometry has been confirmed. Further, the behavior of the radial state parameter ${\omega }_r$, the tangential state parameter ${\omega }_t$, and the anisotropy parameter △ describing the geometry of the universe, has been presented for different values of $\lambda$ chosen in $[-100,100]$.