International Journal of Geometric Methods in Modern Physics

In this paper, we study applications of some certain types of solitons such as conformal Ricci soliton, conformal $\eta$-Ricci–Yamabe soliton and $\eta$-Ricci soliton on Kählerian spacetime manifolds. Further, we have developed the characteristics of conformal Ricci soliton and conformal $\eta$-Ricci–Yamabe soliton on almost pseudo-symmetric Kählerian spacetime manifolds. Here, we have signalized the nature of solitons in terms of shrinking, steady or expanding and we have also presented the relationship between $\lambda$ and $\mu$ in terms of conformal $\eta$-Ricci–Yamabe soliton. Finally, we have embellished the classification of the potential function with respect to gradient $\eta$-Ricci soliton on Kählerian spacetime manifolds.

Kim and Lee [Phys. Rev. D 63 (2001) 064014] studied charged wormholes and Morris–Thorne wormholes in the presence of scalar field using the concepts of general relativity. In this paper, we have also considered same wormholes affected with electric charge and scalar field and extended their study using the framework of $f(R,T)$ gravity with $f(R,T)=R+\beta R^2+\lambda T$ gravity model, where $\beta$ and $\lambda$ are constants. We have examined the possibility for minimization of the amount of exotic matter through energy conditions. Further, we have obtained the deflection angle, an important notion in gravitational lensing, by using strong field limit coefficients which may be helpful in the detection of wormholes.

This paper investigates the wormhole solutions in Rastall theory of gravity using the Karmarkar conditions. For this purpose, we choose a shape function (SF) that connects two asymptotically flat regions. We also discuss the wormhole configuration by plotting three-dimensional (3D) analysis of the embedding diagram in Euclidean space. Furthermore, we also observe the detailed graphical representation of energy conditions using the considered SF. The violation of energy conditions, especially null energy conditions (NEC), indicates the existence of exotic matter and wormholes. Hence, it can be concluded that our calculated results in the background of Rastall theory of gravity are viable and stable. The exciting feature of this work is the 3D analysis to discuss the viability of wormhole geometry

The goal of this paper is to study certain types of metric such as ∗-conformal Ricci–Yamabe soliton (RYS), whose potential vector field is torse-forming on Kenmotsu manifold. Here, we establish the conditions for solitons to be expanding, shrinking or steady and find the scalar curvature when the manifold admits ∗-conformal RYS on Kenmotsu manifold. Next, we developed the nature of the vector field when the manifold satisfies ∗-conformal RYS. Also, we have adorned some applications of torse-forming vector field in terms of ∗-conformal RYS on Kenmotsu manifold. We have also studied infinitesimal CL-transformation and Schouten–van Kampen connection on Kenmotsu manifold, whose metric is ∗-conformal RYS. We present an example of ∗-conformal RYS on three-dimensional Kenmotsu manifold, and verify some of our findings.

In this paper, we investigate almost Schouten solitons and almost gradient Schouten solitons in spacetimes of general relativity. At first, it is proven that if a generalized Robertson–Walker spacetime permits an almost Schouten soliton, then it becomes a perfect fluid spacetime as well as the spacetime represents a dark matter era. Besides this, we investigate almost gradient Schouten solitons in generalized Robertson–Walker spacetimes. Moreover, a spacetime obeying almost Schouten solitons whose potential vector field is a non-homothetic conformal vector field is of Petrov type $O$ or $N$.

The Bekenstein–Hawking entropy of a black hole is proportional to its horizon area, hence in $D=2$ spacetime dimensions it is constant because the horizon degenerates into two points. This fact is consistent with Einstein’s gravity becoming topological in two dimensions. In $F(R)$ gravity, which is non-trivial even in $D=2$, we find that the entropy is constant, as for Bekenstein–Hawking. As shown in Europhys. Lett. 139(6) (2022) 69001, arXiv: 2208.10146, two-dimensional $F(R)$ gravity is equivalent to Jackiw–Teitelboim gravity, in turn, equivalent to the Sachdev–Ye–Kitaev model where the entropy becomes constant in the large $N$ limit. Several recently proposed entropies are functions of the Bekenstein–Hawking entropy and become constant in $D=2$, but in two-dimensional dilaton gravity entropies are not always constant. We study general dilaton gravity and obtain arbitrary static black hole solutions for which the non-constant entropies depend on the mass, horizon radius, or Hawking temperature, and constitute new proposals for a generalized entropy.

Taking wedge products of the $p$ distinct principal null directions (PNDs) associated with the eigen-bivectors of the Weyl tensor associated with the Petrov classification, when linearly independent, one is able to express them in terms of the eigenvalues governing this decomposition. We study here algebraic and differential properties of such $p$-forms by completing previous geometrical results concerning type I spacetimes and extending that analysis to algebraically special spacetimes with at least two distinct PNDs. A number of vacuum and nonvacuum spacetimes are examined to illustrate the general treatment.

The influence of a curved spacetime $M$ on the physical behavior of an ideal gas of $N$ particles is analyzed by considering the phase space of the system as a region of the cotangent bundle $T^{\ast }{M}^N$ and using Souriau’s Lie group thermodynamics to define the corresponding probability distribution function. While the construction of the phase space respects the separability of the system, by forcing each particle to satisfy the so-called mass-shell constraint, the probability distribution is constructed by mixing the natural symplectic structure of the cotangent bundle with a Hamiltonian description of the system. In this way, the spacetime is introduced into the statistics and its isometries turn out to be of special interest because the distributions are parametrized by the elements of the Lie algebra of the isometry group, through the momentum map of the action of the isometries in $T^{\ast }{M}^N$. We find the Gibbs distribution that, in the simplest case of a flat spacetime, reduces to the so-called modified Jüttner distribution, used to describe ideal gases in the regime of special relativity. We also define a temperature-like function using the norm of a Killing vector, which allows us to recover the so-called Tolman–Ehrenfest effect. As a particular example, we study the outer region of a Schwarzschild black hole, for which a power series expansion of the Schwarzschild radius allows us to represent the partition function and the Gibbs distribution in terms of the corresponding quantities of the Minkowski spacetime.

In this paper, we introduce a new vector space, the three-dimensional geometric real vector space ${ℝ}^3(G)$, and a new number system, multiplicative quaternions $ℍ(G)$. We give some basic algebraic properties of these concepts. We define spatial rotation in ${ℝ}^3(G)$ by using multiplicative quaternions. Finally, we give an example to illustrate our results.

In this paper, we investigate the accelerated expansion of the Universe in the context of $f(Q)$ modified theory of gravity, where $Q$ is a non-metricity scalar which characterizes the gravitational interaction by using parametrization of the deceleration parameter $q=\alpha -\frac{\beta }{H}$ with $f(Q)=\xi +\lambda Q$, where $\xi$ and $\lambda$ are free parameters constrained by the 57 points of $H(z)$ datasets, 1048 points of Pantheon, 10 points from Baryon Acoustic Oscillations (BAO) datasets and the shift parameters from Planck 2018 of Cosmic Microwave Background (CMB). In the purpose of validating our model, we proceed by the Om diagnostic and the energy conditions. Later we discussed how our model statistically supports $\mathrm{\Lambda }$CDM using ${\mathrm{\text{AIC}}}_c$ criterion analysis.

We consider it worthy if we could construct a realistic model universe that would enable us to identify a clue about the source of dark energy. So, we develop a Scale Covariant Theory model universe considering a 5D spherically symmetric space-time. It is predicted that the constructed model itself behaves as a phantom energy model/ source that tends to a de Sitter phase avoiding the finite-time future singularity (big rip). The model universe is isotropic and is free from an initial singularity. The gravitational constant $G$ decreases with a variation of $-7.2\times 10^{-11}$${\mathrm{\text{yr}}}^{-1}$ and the Hubble parameter is estimated to be $H=68$. We also provide a thorough analysis of the cosmological findings with graphical representations.

This paper employed the $exp(-\phi (\xi ))$-expansion, Riccati equation, $(G^{\prime }/G)$-expansion, and modified Kudryashov methods to find new exact solution sets for the conformable generalized $(3+1)$-dimensional Camassa–Holm–Kadomtsev–Petviashvili equation. The accuracy of the results has been demonstrated using a variety of graphical representations. These newly obtained solutions can be applied to further research and understand the dynamics of the Camassa–Holm–Kadomtsev–Petviashvili equation, which arises in ocean and water wave theory, hydrodynamics, plasma physics, nonlinear sciences, and engineering. The presented four methods are straightforward, robust, and successful in getting analytical solutions to nonlinear fractional differential equations, as the analytical results indicate.

In this paper, we study the notion of symplectic scalar curvature on the supermanifold over an ordinary Fedosov manifold whose structural sheaf is that of differential forms. In this purely geometric context, we introduce two families of odd super-Fedosov structures, the first one is very general and uses a graded symmetric connection, leading to a vanishing odd symplectic scalar curvature, while the second one is based on a graded non-symmetric connection and has a nontrivial odd symplectic scalar curvature. As a simple example of the second case, we determine that curvature when the base Fedosov manifold is the torus.

Starting from the known condition of Karmarkar, which guarantees that a static and spherically symmetrical space-time is embedded in a manifold of dimension 5, and that it generates a differential equation between the metric coefficients $g_{tt}$ and $g_{rr}$, we solve Einstein’s equations for a fluid with anisotropic pressures. This allows us to represent the interior of the neutron star EXO 1785-248, with observational data around the pair of mass and radius $(M_a=1.4M_{\odot }$, $R_a=11\mathrm{\text{km}})$ and $(M_b=1.7M_{\odot }$, $R_b=9\mathrm{\text{km}})$. It is shown that the density, radial and tangential pressure are monotonically decreasing functions, while the radial and tangential speeds of sound satisfy the causality conditions. The model presented depends on the compactness $u=\frac{GM}{c^{2}R}$ and two other parameters that characterize the internal behavior of the Hydrostatic variables, in particular the values of the central density ${\rho }_c$. In particular for the observational values of mass and radius $(M_a,R_a)$, we have $5.8441\times 10^{17}\frac{\mathrm{\text{kg}}}{{\mathrm{\text{m}}}^3}\lesssim {\rho }_c\lesssim 7.1755\times 10^{17}\frac{\mathrm{\text{kg}}}{{\mathrm{\text{m}}}^3}$ meanwhile that for $(M_b,R_b)$ we have $1.5960\times 10^{18}\frac{\mathrm{\text{kg}}}{{\mathrm{\text{m}}}^3}\lesssim {\rho }_c\lesssim 2.0844\times 10^{18}\frac{\mathrm{\text{kg}}}{{\mathrm{\text{m}}}^3}$. In a complementary manner it is shown that the model satisfies the causality condition and that according to the stability criteria of Harrison–Zeldovich–Novikov and of cracking the solution is stable.

In this report, we present an interior solution to Einstein’s equations in a spherically symmetric and static spacetime filled by two sources with anisotropic pressures, one of these of ordinary matter for which the radial pressure is described by the MIT Bag state equation associated to the presence of quarks and the other by non-ordinary quintessence type matter. The solution is obtained from imposing the Karmarkar condition considering a metric function $g_{rr}={[1+Ca{r}^2{arctan}^2(d+a{r}^2)]}^{-1}$ resulting in a physically acceptable, stable and adequate model to represent compact objects with compactness rate $u=\frac{GM}{c^{2}R}\lesssim \frac{1}{3}$. Which allows to take different value of mass and radius in the range of the observational data of mass $M=(1.74\pm 0.14)M_{\odot }$ and radius $R=9.3\pm 1.0\mathrm{\text{km}}$ of the star 4U1608-52 with compactness $u=0.32044$, from these data we determine the range of $B_g\in [89.85,113.95]{\mathrm{\text{MeV/fm}}}^3$.

This paper retrieves the investigation of rational solitons via symbolic computation with logarithmic transformation and ansatz functions approach for the $(3+1)$-dimensional generalized Konopelchenko–Dubrovsky–Kaup-Kupershmidt (GKDKK) equation in fluid mechanics, ocean dynamics and plasma physics. We find two categories of M-shaped rational solitons and their dynamics will be revealed through graphs by choosing the suitable values of involved parameters. In addition, two categories of M-shaped rational solitons and their interactions with kink waves will be analyzed. Furthermore, homoclinic breathers, multi-wave and kink cross rational solitons will be investigated. The periodic, rational, dark, bright, Weierstrass elliptic function and positive soliton solutions will also be retrieved with the aid of Sub-ODE approach. Moreover, stability characteristics of solutions will be evaluated.

This study presents analytical and numerical solutions of a simplified third-order generalized nonlinear Schrödinger equation (GNLSE) to demonstrate how ultrashort pulses behave in optical fiber and quantum fields. The investigated model can be used as a wave model to illustrate the wave aspect of the matter. It is called a quantum-mechanical state function because it might show how atoms and transistors move and act physically. Four analytical and numerical schemes are used to construct an accurate novel solution. Khater II (Kha II) and novel Kudryashov (NKud) methods are present in the employed analytical scheme. In contrast, the exponential cubic-B-spline and trigonometric-quantic-B-spline schemes represent the simulated numerical techniques. Many novel solitary wave solutions are constructed and formulated in some distinct forms and represented through density, three-, and two-dimensional graphs. The built analytical solutions accuracy is investigated by deriving the requested boundary and initial conditions for implementing the suggested numerical schemes that show the matching between both solutions (analytical and numerical). This matching between solutions proves the accuracy of the obtained solutions. Additionally, to guarantee the applicability of our solutions, we investigate their stability by using the Hamiltonian systems properties. Finally, the novelty of our study and its scientific contributions are illuminated by comparing our results with recently published ones.

We investigate some properties of a black hole in a Horndeski gravity theory mimicking EGB gravity at $D\to 4$. Borrowing ideas from quasitopological gravities provide a matter source of dyonic fields, in which the black hole solution carries two charges, electric and magnetic, in the context of the Einstein–Gauss–Bonnet (EGB) gravity. However, due to several limitations of the EGB gravity in $D\to 4$, we consider a Horndeski gravity theory which can mimic EGB gravity in $D\to 4$. The essential practice used in this paper is the electromagnetic quasinormal modes process, with the goal of discovering the spectrum of such an electromagnetic perturbation over the black hole spacetime. The Wentzel–Kramer–Brillouin (WKB) approximation is used to achieve the desired results. The study shows that both the charges have similar impacts on the quasinormal modes.