International Journal of Geometric Methods in Modern Physics

Employing the Palatini version of $f(R)$ gravity theory ($R$ being the Ricci scalar), this paper describes the evolution of a radiating axially symmetric fluid and its changeover to a non-radiating state. Orthonormal tetrad formalism is taken into account because this technique is easier to use and yields simple tensors leaving the predictions of the theory unchanged. Effective tetrad components of the heat flux, the vorticity vector and the shear tensor are evaluated along with the two parts (electric and magnetic) of Weyl curvature tensor. Furthermore, certain structure scalars are procured from the orthogonal division of the Riemann tensor to figure out basic characteristics of the fluid source like the energy density, stress anisotropy and the heat flux. Few differential equations are worked out to gain insight into the consistency of modified field equations while the system transits from its radiating to equilibrium state.

We find necessary and sufficient conditions for a Finsler surface $(M,F)$ to be Landsbregian in terms of the Berwald curvature $2$-form. We study Finsler surfaces which satisfy some flag curvature $K$ conditions, viz., $V(K)=0,V(K)=-{ℐ}/F^2$ and $V(K)=-{ℐ}K,$ where ${ℐ}$ is the Cartan scalar. In order to do so, we investigate some geometric objects associated with the global Berwald distribution ${𝒟}:=span\{H,S,V:=JH\}$ of a $2$-dimensional Finsler metrizable nonflat spray $S$. We find out under what conditions these surfaces turn out to be Riemannian. The existence of a first integral for the geodesic flow in each case has some remarkable consequences concerning rigidity results. We prove that a Finsler surface with $V(K)=-{ℐ}/F^2$ and either $S(K)=0$ or $S({𝒥})=0$ is Riemannian. Further, a Finsler surface with $V(K)=-{ℐ}K$ and $S(K)=0$ is Riemannian.

There are a number of different theories which tend to explain the concept of universe’s accelerated expansion. Among these theories, modified gravity is the most promising one. This paper elaborates matter distribution along with different characteristics of anisotropic compact stars in $f(R,G)$ gravity background. Specifically, to profoundly understand physical behavior of the compact stars, we considered six compact stars, namely: Her X-1 (${\mathrm{\text{CS}}}_1$), SAXJ1808.4-3658 (${\mathrm{\text{CS}}}_2$), 4U1820-30 (${\mathrm{\text{CS}}}_3$), PSR J 1614 2230 (${\mathrm{\text{CS}}}_4$), VELA X-1 (${\mathrm{\text{CS}}}_5$) and Cen X-3 (${\mathrm{\text{CS}}}_6$) and calculated the corresponding quantities such as energy density ($\rho$), radial pressure ($p_r$) and tangential pressure ($p_t$) using three distinct models of $f(R,G)$ gravity. For simplicity, $f(R,G)$ gravity is divided into two parts as: $f(R,G)=f_1(R)+f_2(G)$. The first part $f_1(R)$ is considered Hu–Sawicki like model, while the second part $f_2(G)$ is considered logarithmic like for Model 1 and power law like for Model 2 and Model 3. Predominantly, measurements of anisotropy, the energy conditions (ECs) and stability aspects of models for considered compacts stars are presented using graphical techniques. Furthermore, we also established that for the $f(G)$ model parameter ($n>0$), all the six stars show conventional behavior.

In this paper, we introduce two new shape functions of wormholes in $f(R,T)$ gravity. Both shape functions are satisfied by various geometric conditions. We will also discuss the different energy conditions and geometric behavior corresponding to each shape function in different states. Finally, we investigate the system’s stability with a solution corresponding to the two shape functions.

In this paper, the effects of strong gravitational lensing are explored in the context of traversable wormholes by determining the existence of photon spheres. The redshift function is defined as $\mathrm{\Phi }(r)=\frac{\xi }{r}+\frac{\eta }{r^2}$, where $\xi$ and $\eta$ are constants. Using this redshift function, the points of maximum potentials are determined which consequently gives the radius of photon spheres. It is obtained that either the throat itself can act as an effective photon sphere or the photon sphere exists outside the throat of the wormhole. Further, the nature of matter supporting the wormhole solutions is examined by analyzing the energy conditions, and the stability of solutions is tested with the help of the TOV (Tolman–Oppenheimer–Volkoff) equation.

We consider a physical system consisting of two interacting spins governed by the $XXZ$-type Heisenberg Hamiltonian in an external magnetic field. We investigate the quantum evolution and the Riemannian geometry of the two-spin state space by means of the relevant Fubini–Study metric. The geometrical phase accumulated by the two-spin state is also examined under arbitrary and cyclic evolutions. By computing the evolution speed and the corresponding geodesic distance, we solve the quantum brachistochrone problem. The entanglement between the two spins is also studied via two approaches: the first one deals with the entanglement effect on the Fubini–Study metric and the geometrical phase, while the second one treats the entanglement effect on the evolution speed and the corresponding geodesic distance. Finally, we solve the quantum brachistochrone problem using the entanglement degree.

In this paper, we obtain the black hole solution for the Ayón-Beato–García (ABG)-type black hole surrounded by a cloud of strings in Rastall gravity and calculate the scalar quasinormal modes of it for a massless scalar field. To have a better visualization of the results, we also introduce a new nonlinear electrodynamic source and obtain a black hole solution surrounded by a cloud of strings in the Rastall gravity. We see that the quasinormal modes are affected by the type of nonlinear electrodynamic sources in case of higher magnitudes of charge $q$. With increase in the magnitude of charge $q$, gravitational waves decay rapidly for the new black hole solution, while for the ABG black hole, the decay rate increases initially and finally starts to decrease near to $q=1$. We also study the impact of the cloud of strings and other model parameters, including the Rastall parameter on the quasinormal modes for both of the black holes. The gravitational waves decay slowly with increase in the cloud of strings parameter for both of the black holes. Dependency of quasinormal modes on the Rastall parameter is different from a surrounding dark energy field and the decay of gravitational waves may be slow or rapid depending on the value of this parameter.

This paper studies thermodynamics of magnetically charged black holes in Anti-de Sitter space in an extended phase space. The cosmological constant is considered as a pressure and the black hole mass is treated as the chemical enthalpy. The black hole thermodynamics is similar to the Van der Walls liquid–gas thermodynamics. Quantities conjugated to the nonlinear electrodynamics parameter and a magnetic charge are obtained. The first law of thermodynamics and the generalized Smarr relation take place. We investigate critical behavior of black holes and Joule–Thomson expansion. The Gibbs free energy, the Joule–Thomson coefficient and the inversion temperature are calculated.

In this paper, we explore traversable wormhole solutions in different cases of modified $F(R,T)$ theories of gravity. We have taken the functional form $F(R,T)=R+\alpha R^2+\lambda T$, where $R$ is Ricci scalar and $T$ is the trace of energy momentum tensor, while $\alpha$ and $\lambda$ are constants. The different forms of $R^2$-gravity in $f(R,T)$, $f(R)$ frameworks and $f(R,T)=R+\lambda T$ gravity are analyzed with its geometric behavior. The energy conditions are also discussed in the isotropic scenario using EoS $\omega =\frac{p_r}{\rho }$ and hybrid shape function $b(r)=\frac{r_0^{2}exp(r_0-r)}{r}$, where $r_0$ is the throat radius. In this investigation, we found that quadratic geometric term and linear trace term of $f(R,T)$ gravity and hybrid shape function play a significant contribution to validate the energy conditions for nonexotic wormhole solutions.

This paper explores the role of nonlinear electrodynamics on the stable configuration of thin-shell wormholes formulated from two equivalent geometries of Reissner–Nordström black hole with nonlinear electrodynamics. For this purpose, we use cut and paste approach to eliminate the central singularity and event horizons of the black hole geometry. Then, we explore the stability of the developed model by considering different types of matter distribution located at thin-shell, i.e. barotropic model and variable equations of state (phantomlike variable and Chaplygin variable models). We use linearized radial perturbation to explore the stable characteristics of thin-shell wormholes. It is interesting to mention that Schwarzschild and Reissner–Nordström black holes show the unstable configuration for such type of matter distribution while Reissner–Nordström black hole with nonlinear electrodynamics expresses stable regions. It is found that the presence of nonlinear electrodynamics gives the possibility of a stable structure for barotropic as well as variable models. It is concluded that stable region increases for these models by considering higher negative values of coupling constant $\alpha$ and the real constant $n$.

In this work, we study the relativistic quantum motions of spin-zero scalar massive charged bosons in a topologically nontrivial four-dimensional rotating space-time in the presence of a uniform magnetic field and quantum flux. Afterwards, a spin-zero relativistic quantum oscillator model is also studied and determines the bound-state eigenvalue solutions of the quantum system. We see that the energy eigenvalue and the wave function get modified by the nontrivial topology of the geometry, the rotating frame of reference, and the magnetic field. We also observed the gravitational analog of the Aharonov–Bohm (AB) effect due to the dependence of the energy eigenvalue on the geometric quantum phase.

The purpose of this paper is to investigate proper conformal vector fields (CVFs) of Bianchi type-I perfect fluid space-times in the $f(R$, $T)$ theory of gravity, where $R$ and $T$ are the Ricci scalar and the trace of energy–momentum tensor, respectively. To seek the proper CVFs, we perform a classification of the space-times by imposing different restrictions on the space-time components. The whole classification consists of 12 cases. By studying each case thoroughly, we conclude that in the $f(R$, $T)$ theory of gravity, the overall dimension of CVFs for the Bianchi type-I space-times turns out to be 3, 4, 5 and 15.

The scope of this work is based on symmetry analysis of perturbed fractional Boussinesq equation. For beginning the group formalism, invariance properties and conservation laws of the nonlinear perturbed fractional Boussinesq equation have been explored generally. This method was first described by Lukashchuk [Commun. Nonlinear Sci. Numer. Simul. 68 (2019) 147–159]. The key subject is that when the order of fractional derivative in a fractional differential equation (FDE) is nearly integers, we can approximate it to a perturbed integer-order differential equation with a small perturbation parameter. For obtaining the results, perturbed and unperturbed symmetries are computed. Then, the methodology of reduction is applied for finding some new solutions by the symmetry operators of the equation. These solutions are obtained by the similarity transformations of the symmetries. Another exact solution will be found with constructing one-dimensional optimal system of the symmetries. Finally, the meaning of nonlinear self-adjointness concept is attended in order to find conservation laws with informal Lagrangians.

The present analysis deals with the wormhole (WH) solutions in $f(\mathcal{ℛ},\phi ,\chi )$ gravity, where $\mathcal{ℛ}$, $\chi$ and $\phi$ represent the Ricci scalar, kinetic expression and potential field, respectively. To complete this analysis, we use the WH geometry via spherical spacetime with the anisotropic matter distribution. Further, we consider the Gaussian distribution as non-commutative geometry to complete the analysis under conformal symmetry. We calculate the exact WH shape function by plugging the possible conformal Killing vectors. Further, we have discussed the embedded surface to understand the WH geometry. Furthermore, the Tolman–Oppenheimer–Volkoff equation is considered to discuss the stability of WH configuration with the Gaussian energy density source.

In this paper, we characterize three-dimensional Riemannian manifolds $M^3$ admitting Ricci–Yamabe solitons (RYSs). It is proved that if an $M^3$ endowed with a semi-symmetric metric $\zeta$-connection admits an RYS, then the scalar curvature of $M^3$ satisfies the Poisson equation $\mathrm{\Delta }r=\frac{8(2\alpha -3\beta -\varrho )}{\beta },$ where $\alpha ,\beta \in ℝ$ and $\beta \ne 0.$ We also discuss the existence of gradient RYS in Riemannian setting. Finally, we construct a nontrivial example of three-dimensional Riemannian 3-manifolds admitting RYS to prove some of our results.

We discuss the application of quaternionic space-time algebra for the generalization of self-consistent equations describing the hydrodynamic two-fluid model of vortex plasma. It is shown that quaternionic formalism allows one to write the system of hydrodynamic equations in a compact form as one quaternion equation, which can be easy generalized to the case of damping plasma in an external electromagnetic field. As an illustration, we apply the proposed equations for the description of sound waves in electron–ion and electron–positron plasmas.

In continuation to the recent study “Coupled Fractional Wigner Distribution with Applications to LFM Signals” in [Fractals, World Scientific; 2022], we formulate some important uncertainty inequalities including, the Hausdorff–Young, Lieb’s and Pitts inequalities for the coupled fractional Wigner distribution. In the sequel, we also establish Heisenberg’s, logarithmic, Hardy’s and Beurling’s uncertainty principles. Towards the end, we derive some Sobolev-type inequalities for the coupled fractional Wigner distribution.

Einstein’s field equations not only allow realistic solutions, but also allow exotic ones. In the first class, there are solutions describing FLRW universe, black holes and the gravitational waves. In the second class, we point out de Sitter and Anti-de Sitter universes without matter, wormholes solutions and Gödel universe without time. In this paper, we are interested in finding out a simpler example of Gödel-type universe. The road to the desired result passes through a spacetime without matter and time at the same time, whose texture is “flicked” by planar gravitational waves. This example allows us to create a simpler Gödel-type universe.