International Journal of Geometric Methods in Modern Physics

In this work, for the first ever, the fractal Konopelchenko–Dubrovsky equations is defined by using a new fractional derivative called $M$-truncated fractional derivative. The main goal of this work is to seek new type of fractal solitary wave solutions for the fractal Konopelchenko–Dubrovsky equations by a novel mathematical scheme, which is called variational sech-function method. The forms of these new fractal solitary wave solutions are different from those in the existing literature. Ultimately, the fractal dynamic behavior of these derived fractal solitary wave solutions is illustrated via a number of 3D and 2D simulation graphs with different parameters and fractal dimensions. The proposed new method can be employed to other nonlinear wave equations in mathematical physics with the same fractional derivative.

In this study, unimodular $f({𝒢},T)$ gravity is proposed as an alternative theory of gravity. Field equations of unimodular $f({𝒢},T)$ gravity are suggested. The field equation and their solutions are obtained for exponential expansion and power-law expansion models. Energy conditions of unimodular $f({𝒢},T)$ gravity are defined by using Raychaudhuri equations. Energy conditions for exponential expansion and power-law expansion models are investigated. Hubble parameter and deceleration parameter are calculated by considering power-law expansion model and obtained solutions. It has been shown that both deceleration parameter and Hubble parameter are compatible with the current observational data.

We investigate Kaniadakis holographic dark energy (KHDE) model taking the apparent horizon as the IR cutoff in a flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. We apply variant dark energy (DE) diagnostic tool to study KHDE model in flat universe with different values of the constant $C^2$ and Kaniadakis entropy parameter $k$. We use the tools statefinder hierarchy $(S_3^{(1)},S_3^{(2)},S_4^{(1)},S_4^{(2)})$, fractional growth parameter $𝜖$ and composite null diagnostic (CND), which is blend of $(S_3^{(1)},(S_4^{(1)})$ and $𝜖$. The evolution of trajectories of $S_3^{(1)},S_3^{(2)},S_4^{(1)}$ and $S_4^{(2)}$ depicts that there occur degeneracies in early time and also in the far future, whereas, in between these two extremes they are discriminated distinctly. The analysis of the present work shows that by the inclusion of fractional growth parameter $𝜖$ with statefinder hierarchy (CND) degeneracy is removed reasonably, particularly more in the low redshift region.

Horizonless compact objects with light rings are becoming more popular in recent years for numerous motives. In this paper, the conditions under which the throat of a Morris–Thorne wormhole can act as an effective photon sphere are worked out. A specific example which satisfies all the energy conditions in modified theory of gravity is considered and the formation of relativistic images is studied. We have detected photon spheres for the wormhole modeling due to the effect of strong gravitational lensing. Subsequently, we have found the expression for deflection angle in terms of the angular separation between the image and lens by determining the strong-field limit coefficients. It is found to diverge for the impact parameter corresponding to the photon sphere. We observed that the angle of Einstein ring ${𝜃}_0$ and relativistic Einstein ring ${𝜃}_{n\ge 1}$ are completely distinguishable. Given the configuration of the gravitational lensing and the radii of the Einstein ring and relativistic Einstein rings, we can distinguish between a black hole and a wormhole in principle. The stability of wormholes is examined from the positivity of the shape function and satisfaction of the flare-out condition.

We show that each irreducible tensor representation of weight 2 of the rotation group in the space of rank 3 tensors over three-dimensional space gives rise to an associative algebra with unity. We find the algebraic conditions to be satisfied by the generators of these algebras. Part of these relations is of binary, and another part is of ternary type. The structure of the latter one is based on the use of the cyclic group ${\mathbb{Z}}_3$ generated by the primitive cubic root of unity given by $q=exp(2\pi i/3)$. The subspace of each algebra spanned by triple products of generators is five-dimensional (5D) and is identical with the space of irreducible tensor representation of weight 2 of the rotation group $\mathrm{\text{SO}}(3)$. We define a Hermitian scalar product in this 5D subspace and construct its orthonormal basis in terms of triple products of generators. Then we find an explicit formula for the Lie algebra homomorphism $\mathrm{\text{so}}(3)\to \mathrm{\text{su}}(5)$. We suggest that the algebras constructed in this way, with binary and ternary constitutive relations, may find applications in the quark model and the Grand Unified Theories.

The $(2+1)$-dimensional chiral nonlinear Schrödinger equation (CNLSE), which specifies the edge states of the Hall effect, is presented in this study. A complicated transformation is performed, and the bifurcation conditions are determined using the theory of planar dynamical systems. The phase pictures of the system are then produced using quantitative analysis in order to predict the family of solutions which can be found for the equation studied. It is important to note that this prediction is usually not made. The qualities of phase pictures are then used to obtain the exact solutions. As a result, this model produces some bright solitons, dark solitons and periodic wave solitons. Some of the solutions are graphically depicted in three dimensions (3D) using Matlab software to aid comprehension, and they play an important part in the creation of realistic Quantum Hall effects when Chiral excitations are known to occur. The method applied in this paper is simple and does not need an ansatz to predict the solutions as in the literature.

We construct the novel Clifford-Yang algebra which is an extension of the Yang algebra in noncommutative phase spaces. The Clifford-Yang algebra allows us to write down the commutators of the $noncommutative$ polyvector-valued coordinates and momenta which are compatible with the Jacobi identities, the Weyl–Heisenberg algebra, and paves the way for a formulation of quantum mechanics (QM) in noncommutative Clifford spaces. We continue with a detailed study of the isotropic 3D quantum oscillator in noncommutative spaces and find the energy eigenvalues and eigenfunctions. These findings differ considerably from the ordinary quantum oscillator in commutative spaces. We find that QM in noncommutative spaces leads to very different solutions, eigenvalues, and uncertainty relations than ordinary QM in commutative spaces. The generalization of QM to noncommutative Clifford (phase) spaces is attained via the Clifford-Yang algebra. The operators are now given by the generalized angular momentum operators involving polyvector coordinates and momenta. The eigenfunctions (wave functions) are now more complicated functions of the polyvector coordinates. We conclude with some important remarks.

In this paper, we have studied Kaluza–Klein Cosmological Model with strange-quark-matter in Lyra Geometry. To determine the solution of the field equation, we have assumed that scalar expansion $𝜃$ is proportional to shear scalar ${\sigma }^2$ which leads to $A_1={(A_2)}^r$, where $A_1$, $A_2$ are metric potentials and $r$ is arbitrary constant. The cosmological parameters are investigated with the help of equation of state strange-quark-matter (SQM), which is $p=\frac{\rho -4B_c}{3}$, where $B_c$ is Bag constant. We compared the results of general General relativity (GR) and scalar-tensor theory and also discussed the behaviors of some physical parameters.

In this work, we examine the Joule–Thomson (JT) expansion for a nonlinearly charged AdS black hole solution. We obtain the expression of the JT coefficient from which we calculate the inversion temperature for numerous values of the charge $Q$. Moreover, we derive the isenthalpic curve in $(T,P)$ diagram and illustrate the cooling–heating region by the inversion curve for fixed masses. We find that the temperature and pressure on the inversion point decrease with a larger charge $Q$ and increase as the black hole mass grows.

In this paper, we analyze the modification to the thermodynamics of a Schwarzschild black hole and a Kerr black hole due to gravity’s rainbow. The metric for these black holes will be made energy dependent. This will be done by using rainbow functions motivated from the hard spectra from gamma-ray bursters at cosmological distances. This modification of the metric by these rainbow functions will in turn modify the temperature and entropy of these black holes. We will also discuss how this affects the formation of virtual black holes.

Holographic dark energy (HDE) models are significantly different from standard dark energy (DE) models since they are based on holographic principles rather than mentioning a term in Lagrangian. Nojiri et al. [Barrow entropic dark energy: A member of generalized holographic dark energy family, Phys. Lett. B 825 (2022) 136844] proposed a generalized Barrow HDE (BHDE) model depending on particle horizon and future horizon, where the infra-red cut-off is considered as a usual cut-off. In this paper, we have revisited the generalized BHDE adopting the Granda–Oliver cut-off as the standard cut-off for the model. We have generalized BHDE behaviors with two different cut-offs, future horizon $L_f$ and particle horizon $L_p$. The holographic cut-off is extended to depend on $L_{\mathrm{\text{GO}}}=L_{\mathrm{\text{GO}}}(L_p,{\dot{L}}_p,{\ddot{L}}_p,\dots ,L_f,{\dot{L}}_f,\dots ,a)$, where a is the scale factor. Using this formalism, we demonstrated that the Barrow entropic DE model is equivalent to the generalized HDE model, where two ways are used to compute the respective holographic cut-off: first, in terms of particle horizon and its derivative, and second, future horizon and its derivative. We use 57 observational data points to determine the current Hubble constant $H_0$. We have studied the behavior of few quantities, such as DE density $({\rho }_{\mathrm{\text{de}}})$, pressure $(p_{\mathrm{\text{de}}})$, equation of state (EoS) parameter under the observational data. Here, we have to find the EoS parameter for generalized HDE, equivalent to Barrow entropic DE model. Besides this, we have also discussed k-essence and tachyon DE models.

In this paper, we have explored the field equations of $f(T,B)$ gravity as an extension of teleparallel gravity in an isotropic and homogeneous space-time. In the basic formalism developed, the dynamical parameters are derived by incorporating the power law and exponential scale factor function. The models show accelerating behavior and approach $\mathrm{\Lambda }$CDM at late time. The present value of the equation of state parameter for both the cases is obtained to be in accordance with the range provided by cosmological observations. The geometrical parameters and the scalar field reconstruction are performed to assess the viability of a late-time accelerating universe. Further, the stability of both the models is presented. It has been observed that both the models are parameter-dependent. Since most of the geometrically modified theories of gravity favor the violation of strong energy condition (SEC), we have derived the energy conditions both for the power law and exponential model. In both the models, the violation of SEC is established.

In this paper, we investigate the dynamic evolution of universe in the models of holographic dark energy with $f(Q,T)$ gravity framework where, $Q$ is the non-metricity scalar and $T$ is the energy–momentum tensor trace. We have considered $f(Q,T)=\alpha Q+\beta T$ framework and investigated the evolution of cosmological quantities like energy density, equation of state (EoS) parameter and classical stability parameter with redshift. We parameterize the deceleration parameter and confront the Hubble parameter with the observational data. We investigate for the late-time accelerated expansion of universe and discuss the stability of the model by using adiabatic sound speed squared parameter. A comparison among these derived models suggest that the Renyi holographic dark energy model with GO cutoff satisfies the observational constraint of Planck+SNe+BAO on EoS parameter at present time as compared to other models. Diagnostic tools such as Statefinders and Om diagnostic have been used to classify the dark energy evolution regions.

In this work, new Tsallis holographic dark energy with apparent horizon as IR-cutoff is constructed in a non-flat Friedmann–Lemaitre–Robertson–Walker Universe. The accelerating expansion phase of the Universe is described by using deceleration parameter, equation of state parameter and density parameter by using different values of new Tsallis holographic dark energy (NTHDE) parameter “$\delta$”. The NTHDE Universe’s transition from a decelerated to an accelerated expanding phase is described by the smooth graph of deceleration parameter. Depending on distinct values of Tsallis parameter “$\delta$”, we have explored the quintessence behavior of the equation of state parameter. We used Hubble data sets obtained using Cosmic Chronometric methods and distance modulus measurement of Type Ia Supernova to fit the NTHDE parameters. Stability of our model by analyzing the squared speed of sound is investigated as well.

In this paper, we investigate the thermodynamics of a dark energy bulk viscosity model as a cosmic fluid. In this regard, the two theories of Eckart and Israel–Stewart (IS) are the bases of our work. Therefore, we first investigate the thermodynamics of cosmic fluids in the dark energy bulk viscosity model and the general relationships. Then, we express the thermodynamic relationships of Eckart’s theory. Due to the basic equations of Eckart’s theory and Friedmann’s equations, we consider two states, one is $p=-\rho$ (standard) and the other is $p\ne -\rho$ (non-standard). In the standard state, we define the pressure $(p)$, energy density $(\rho )$ and bulk viscosity coefficient $(\xi )$ of the cosmic fluid in terms of cosmic time and we obtain its relations. We also mention that in this standard state, because of $p=-\rho$, the value of $a(t)$ is zero, so $a(t)$ is not defined in this state. But in the non-standard case $(p\ne -\rho )$, the bulk viscosity coefficient $(\xi )$ is zero and only the scale factor, pressure and energy density of the cosmic fluid are defined. We also consider two states of constant and variable bulk viscosity coefficients and obtain three Hubble constant parameters and scale factor in terms of cosmic time, and energy density in terms of scale factor. In the state of variable bulk viscosity coefficient, we consider the viscosity coefficient as the power law from energy density $(\xi =\alpha {\rho }^s)$, which is $\alpha >0$ and a constant. Following this, we discuss about the dissipative effects of cosmic fluids and examine the effects of energy density for dark energy in the IS theory. The results are comprehensively presented in Tables 1 and 2. Also, according to observational constraints, the results of the likelihood analysis for the IS viscous model are summarized in Table 3.

The class of Petrov type I curvature tensors is further divided into those for which the span of the set of distinct principal null directions has dimension 4 (maximally spanning type I) or dimension 3 (nonmaximally spanning type I). Explicit examples are provided for both vacuum and nonvacuum spacetimes.

In this work, we give a detailed description and discussion of the dynamic gravitational equations of the model with Lagrangian of the type $\int \sqrt{det{R}_{\mu \nu }}{d}^{4}x$ as proposed by Eddington time ago but with $R_{\mu \nu }$ being a non-Riemannian generalization of the Ricci tensor with the end to find the geometrical origin of the Eddington and Weyl conjectures concerning Lagrangian densities (generalized volume) and natural gauge. The Ricci tensor in our case is particularly based on an affine geometry with a generalized compatibility condition previously proposed in [B. McInnes, On the geometrical interpretation of ‘non-symmetric’ space-time field structures, Class. Quantum Grav. 1 (1984) 105–113; D. J. Cirilo-Lombardo, Non-Riemannian geometry, Born–Infeld models and trace-free gravitational equations, J. High Energy Astrophys. 16 (2017) 1–14]. Specifically, we show that: (i) the geometric action can be taken to a BI-type form considering a totally antisymmetric torsion field, (ii) Weyl’s proposal considering a universal gauge linked to a cosmological constant $\lambda$ appears in the model naturally due to the proposed affine geometry, (iii) the Eddington conjecture that establishes a relationship between metric and curvature or fundamental tensor with constant of proportionality $\lambda$ (natural gauge) is geometrically verified in the model with generalized affine geometry.

In this offering exposition, we intend to study paracontact metric manifold $M$ admitting almost Yamabe solitons. First, for a general paracontact metric manifold, it is proved that $V$ is Killing if the vector field $V$ is an infinitesimal contact transformation and that $M$ is $K$-paracontact if $V$ is collinear with Reeb vector field. Second, we proved that a $K$-paracontact manifold admitting a Yamabe gradient soliton is of constant curvature $-1$ when $n=1$ and for $n>1$, the soliton is trivial and the manifold has constant scalar curvature. Moreover, for a paraSasakian manifold admitting a Yamabe soliton, we show that it has constant scalar curvature and $V$ is Killing when $n>1$. Finally, we consider a paracontact metric $(\kappa ,\mu )$-manifold with a non-trivial almost Yamabe gradient soliton. In the end, we construct two examples of paracontact metric manifolds with an almost Yamabe soliton.