International Journal of Geometric Methods in Modern Physics

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 $g_{rr}$ 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 which is physically reasonable and well behaved inside the stellar interior. Interior spacetime has been matched smoothly to the exterior Schwarzschild vacuum solution and it has also been depicted graphically. Model is free from all types of singularities and is in static equilibrium under different forces acting on the system. The stability of the model has been tested with the help of various conditions available in literature. The solution is compatible with observed masses and radii of a few compact stars like Vela X-1, 4U $1608-52$, PSR J$1614-2230$, LMC X $-4$, EXO $1785-248$.

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. Further, the gravitational lensing effect is analyzed by determining the deflection angle in terms of strong field limit coefficients.

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 phases of T - timelike magnetic particle evolutions. Finally, we obtain some numerical modeling of optical magnetic spherical Heisenberg ferromagnetic flows.

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.

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 and AdS–Reissner–Nordström-like black hole spacetimes are achieved. Equations of motion are derived by using Hamiltonian. Orbits of massless test particles are depicted. Obtained line element asymptotically converges to dS/AdS spacetime. Weak and strong energy conditions of the massless scalar field are obtained with Raychaudhuri equations in unimodular $f(R)$ theory. Also, stiff fluid interpretation of scalar field is reviewed.

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.

The aim of this paper is to obtain some results for quotion Yamabe solitons with concurrent vector fields. We prove quotion Yamabe soliton $(M^n,g,v^T,\lambda )$ on a hypersurface in Euclidean space ${ℝ}^{n+1}$ contained either in a hyperplane or in a sphere ${𝕊}^n$.

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 parameter that is inversely proportional to the Hubble parameter. The exact solution of the field equations has been derived. The kinematic and dynamical quantities of the model have been obtained and their evolutions have been discussed by means of their graphs. The statefinder diagnostic has been used and the age of the universe has been computed for testing the validity of the model. It has been shown that the dominant energy of the model is ordinary matter which behaves as the SCDM model at the beginning and it is a quintessence like fluid which behaves as the $\mathrm{\Lambda }$CDM model at late times.

We prove the existence and uniqueness of Levi-Civita connections for strongly $\sigma$-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, Lett. Math. Phys. 110 (2020) 835–884] and [J. Bhowmick, D. Goswami and G. Landi, On the Koszul formula in noncommutative geometry, Rev. Math. Phys. 32(10) (2020) 2050032].

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 $p=(\gamma -1)\rho$ with $\frac{2}{3}\le \gamma \le 2$. By taking the Hubble horizon as the boundary of the universe, we investigate the first and generalized second law of thermodynamics along with thermodynamic equilibrium in the presence of Bekenstein entropy. In order to view the clear picture of these laws, we take into account two models of particle creation rate $\mathrm{\Gamma }$ which are constrained with recent observational data. It is found that the validity of these laws holds for the suitable values of model parameters in the specific ranges of redshift parameter for both models.

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 definition of the average connection does not make use of ${𝒳}$. Therefore, there is no direct relation between these two averaged objects.

In this paper, we examine the functional forms of the potentials $W(u,v,x^A)$ 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 provide a complete analysis of the potentials of this spacetime, which are split into 14 isometry categories.

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 direct integration technique, we find that there exists only one case for which the space-time admits proper CVFs whereas in rest of the cases, the space-time either becomes flat or it admits homothetic vector fields (HVFs) or Killing vector fields (KVFs). The overall dimension of CVFs for the pp-waves space-times in the IDG has turned out to be one, two, seven or fifteen.

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 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 equations by an inheritance symmetry. We study several cases of interest to explore physically valid features of the solutions. Some physical properties of the model are discussed and we match our interior spacetime to the exterior Reissner–Nordström spacetime in presence of thin shell.

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 implies that a transition to a Type II singularity can take place, in a finite time. We take into account a bulk viscosity of the dark fluid, observing the equation of state in the case of radiation, and find that there is a qualitative change in the singular universe of Type I: it may pass into a singularity of Type III, or it may avoid the singularity at all.

In this paper, we derive the necessary and sufficient conditions of surface pencil pair interpolating Bertrand pair as common asymptotic curves in Galilean space G₃. Moreover, the conclusion to ruled surface pencil pair is also obtained. And the examples are given to confirm that the proposed methods are effective in product manufacturing by adjusting the shapes of the surface pencil pair.