International Journal of Geometric Methods in Modern Physics

In this paper, we first introduce a new notion $\beta$-tensor on Hermitian manifold and particularly, we present some geometric characterizations of such a tensor on the Kaehler manifold. Here, we investigate the Kaehler submersion whose total space is equipped with the $\beta$-tensor and obtain some results. Also, we deal with a Kaehler submersion with totally geodesic fibers such that the total space admits ${}^{\ast }$-Ricci soliton and $\beta$-tensor. Finally, we give necessary conditions for which any fiber and base manifold of Kaehler submersion is ${}^{\ast }$-Ricci soliton or ${}^{\ast }$-Kaehler-Einstein.

In this work, a new model of double-Logarithmic electrodynamics has been minimally coupled to Einstein-massive gravity and the nonlinearly charged black holes in the presence of quintessential cosmic dark energy and string cloud background are investigated. In this set up, new magnetically charged black hole solution has been derived. Thermodynamics of these black holes are also analyzed and different thermodynamic quantities are computed. Basic thermodynamic quantities such as heat capacity and Hawking temperature have been plotted and the regions corresponding to thermodynamic stability and instability are pointed out. The generalized first law of thermodynamics and the associated Smarr’s relation have also been written down in this context of massive gravity and matter sources. At last, the nonlinearly electrically charged black holes are also briefly studied.

In this study, we firstly characterize modified magnetic particles and associated magnetic fields by considering the evolution of the charged particle together with its modified frame construction in 3D space. Then, we compute the energy flows of each modified magnetic particles in terms of its curvature and torsion in the space. Finally, we obtain energy flux density, the intensity of the light, power of modified magnetic particles in the space.

The strange quark matter (SQM) for which the distribution is governed by the equation of state of the simplified MIT bag model such as: $p_r=\frac{1}{3}(\rho -4B)$, with $B$ the bag constant, in the presence of a load distribution given by $q(r)=Q{(r/R)}^3=\alpha r^3$ has been the subject of a series of investigations within the framework of Rastall–Maxwell theory. We used the Modified Tolman–Oppenheimer–Volkoff (TOV) equation in Rastall gravity to generate the solutions by make using the conformal Killing vector. In order to check the physical acceptability of our solutions from conformal Killing vector method, we investigated around the Energy conditions, the Mass–Radius relation, Modified TOV equation, redshift and the stability of the system through Adiabatic Index, the Compactification factor and Causality condition. For physical values of Rastall parameters, we noticed that the stellar systems become more massive in proportion to their size. Then, this leads them into less dense compact objects which reveals that the alternative theory of Rastall is appropriate to better explain the behavior of massive stellar objects.

In this work, we study the modified Klein–Gordon oscillator by replacing the momentum vector $\overrightarrow{p}\to (\overrightarrow{p}-iM\mathrm{\Omega }f(r)\widehat{r})$ in the Klein–Gordon equation under scalar and electromagnetic potentials in a rotating cosmic string space-time. The electromagnetic and scalar potentials are chosen to be proportional to the inverse of the axial distance $(\propto \frac{1}{r})$. We solve the radial wave equation and obtain the energy eigenvalues and the corresponding wave function which depend on the global parameters of the space-time, and observe a gravitational analogue of the Aharonov–Bohm effect. We also see that the presence of electromagnetic and scalar potentials allows the formation of the bound-state solutions and the angular frequency of the oscillator depends on the quantum numbers of the system.

Motivated by recent astrophysical observations, we investigate the shadow behaviors of four-dimensional charged rotating black holes with a cosmological constant. This study is made in terms of a reduced moduli space parameterized by the charge and the rotation parameters. For fixed observers, we analyse in some details the shadow behaviors and the corresponding naked singularities of Kerr–Newman and Kerr–Sen four-dimensional black holes in Anti-de Sitter backgrounds. Then, a comparative discussion is provided by computing the geometrical observables and the energy emission rate.

The objective of this paper is to deal with Kenmotsu manifolds admitting $\eta$-Ricci-Yamabe solitons. First, it is proved that if a Kenmotsu manifold $M$ which admits an $\eta$-Ricci-Yamabe soliton, then the manifold $M$ is Einstein and is of constant scalar curvature. Then, some important characterizations, which classify Kenmotsu manifolds admitting such solitons, are obtained and an example given which supports our results.

In this paper, we give an analogue of the Hermitian structure in the almost complex case, on an $n(k+1)$-dimensional manifold endowed with an almost $k$-complex metric. Also, we study the compatibility between Riemannian metric and polarized $k$-symplectic structure. Also, we study some properties of an almost $k$-complex structure. Moreover, we give an equivalence between almost $k$-complex structures, $k$-almost tangent structures and $k$-almost cotangent structures.

A spherical planetary nebula is described as a geometric model. The nebula itself is considered as a thin-shell, which is visualized as a boundary of two spacetimes. The inner and outer curvature tensors of the thin-shell are found in order to get an expression of the energy-momentum tensor on the thin-shell. The energy density and pressure expressions are derived using the energy-momentum tensor. The time evolution of the radius of the thin-shell is obtained in terms of the energy density. The model is tested by using a simple power function for decreasing energy density and the evolution pattern of the planetary nebula is attained.

In this work, we revisit the shear-free conjecture of general relativity and study the well-known shear-free condition in the context of the Chaplygin-gas cosmology. It had been shown in previous investigations that, in the general relativistic framework, the matter congruences of shear-free perfect fluid spacetimes should be either expansion-free or rotation-free. Our current investigation, however, indicates that a universe dominated by a Chaplygin-gas can allow a simultaneous expansion and rotation of the fluid provided that certain non-trivial conditions, which we derive and describe in what follows, are met. We also show that, in the appropriate limiting cases, our results reduce to the expected results of dust spacetimes which can only expand or rotate, but not both, at the same time.

This paper is focused on the study of charged wormholes which are combinations of Morris–Thorne wormhole and Reissner–Nordström spacetime. Gravitational lensing is an important tool which has been adopted to detect various objects like wormholes using the notion of deflection angle. In this work, we have evaluated deflection angle with and without using the strong field limit coefficients and compared the results. Further, exact charged wormhole solutions are obtained in $f(R,T)$ gravity and the nature of the energy conditions is examined.

In this paper, we study connections on hermitian modules, and show that metric connections exist on regular hermitian modules; i.e. finitely generated projective modules together with a non-singular hermitian form. In addition, we develop an index calculus for such modules, and provide a characterization in terms of the existence of a pseudo-inverse of the matrix representing the hermitian form with respect to a set of generators. As a first illustration of the above concepts, we find metric connections on the fuzzy sphere. Finally, the framework is applied to a class of noncommutative minimal surfaces, for which there is a natural concept of torsion, and we prove that there exist metric and torsion free connections for every minimal surface in this class.

In this paper, we have investigated some recently proposed entropy-based versions of various HDE models, namely, the TADE, THDE, RHDE and SMHDE for different values of model parameter $\delta$ with the help of two diagnostic tools, in the context of a flat Friedmann–Lema$î$tre–Robertson–Walker Universe. The statefinder hierarchy is the first diagnostic tool, by which we examine these DE models. The evolution of statefinder hierarchy parameters $S_3^1$, $S_3^2$ $S_4^1$, $S_4^2$ has been investigated by plotting against redshift $z$. The evolutionary trajectories of all the DE models approach the $\mathrm{\Lambda }$CDM model, except the TADE model for some values of $\delta$ at late time, are well discriminated with the $\mathrm{\Lambda }$CDM model at early time. To get more clear discrimination among the DE models at late time, we have used the CND, i.e. $\{S_3^{(1)},𝜖\}$$\{S_4^{(1)},𝜖\}$, where $𝜖$ indicates the fractional growth parameter. The evolutionary trajectories of $\{S_3^{(1)},𝜖\}$ and $\{S_4^{(1)},𝜖\}$ show different characteristics and the departure from $\mathrm{\Lambda }$CDM could be well evaluated.

The aim of this paper is to characterize paracontact metric manifolds admitting Yamabe and quasi-Yamabe solitons. Several results of such solitons are proved. In particular, we classify Yamabe and quasi-Yamabe solitons on $(k,\mu )$-paracontact metric manifolds.

In this paper, we study the generic action for the scale-invariant theory of gravity and then by making use of the holographic methods, we compute some specific holographic measures of entanglement. Precisely, we calculate the entanglement entropy, mutual and tripartite information and show that the mutual information is always positive while the tripartite information becomes negative. This indeed recovers the monogamy property of mutual information in this context.

In this paper, we consider a class of cosmological fluids that possess properties analogous to those of crystalline solids undergoing isotropic deformations. Our research is based on a modified log-corrected power-law equation of state in the presence of a bulk viscosity. This formalism represents a class of the so-called logotropic fluids, and allows explaining an accelerating late-time universe. In order to obtain a more detailed picture of its evolution, we add in our model a coupling of the log-corrected power-law fluid to dark matter, and study various interacting forms between them. We solve the system of equations for a modified log-power-law fluid coupled to dark matter, and obtain expressions for the log-corrected power-law energy density, and the energy density for dark matter. A comparative analysis is made with the model of a nonviscous log-corrected power-law fluid without interaction with dark matter.

In this work, according to the generalized uncertainty principle, we study the Klein–Gordon equation interacting with the electromagnetic field. The generalized Klein–Gordon equation is obtained in the presence of a scalar electric potential and a uniform magnetic field. Furthermore, we find the relation of the generalized energy–momentum in the presence of a scalar electric potential and a uniform magnetic field separately.

Recently, it was shown that the conserved charges of asymptotically anti-de Sitter spacetimes can be written in an explicitly gauge-invariant way in terms of the linearized Riemann tensor and the Killing vectors. Here, we employ this construction to compute the mass and angular momenta of the $D$-dimensional Kerr-AdS black holes, which is one of the most remarkable Einstein metrics generalizing the four-dimensional rotating black hole.