International Journal of Geometric Methods in Modern Physics

Motivated by Dark Energy (DE) activities, we study certain physical behaviors of the quintessential Hayward-AdS black holes in four dimensions. We generalize some physical properties of the ordinary Hayward-AdS black holes without the dark sector. We elaborate a study in terms of the new quantities $c$ and ${\omega }_q$ parametrizing the dark sector moduli space. We investigate the effect of such parameters on certain thermodynamic and optical aspects. To show the quintessential thermodynamic behaviors, we first reconsider the critical properties of the ordinary solutions. We find that the equation of state predicts a universal ratio given by ${\chi }_0=\frac{P_c{v}_c}{T_c}=\frac{27-3\sqrt{6}}{50}$, which is different than the universal one appearing for Van der Waals fluids. Considering the quintessential solutions and taking certain values of the DE state parameter ${\omega }_q$, we observe that the new ratio depends on the DE scalar field intensity $c$. In certain regions of the moduli space, we show that this ratio can be factorized using two terms describing the absence and the presence of the dark sector. Then, we analyze also the DE effect on the heat engines. For the optical aspect, we study the influence of DE on the shadows using one-dimensional real curves. Finally, we discuss the associated energy emission rate, using the dark sector.

We compare in some detail Polymer Quantum Mechanics and the Generalized Uncertainty Principle approach to clarify to what extent we can treat them on the same footing. We show that, while on a semiclassical level they may be formulated as similar modifications of the Poisson algebra, on a quantum level they intrinsically differ because PQM implies no absolute minimal uncertainty on position. Then we implement these schemes to Bianchi I cosmology on a semiclassical level deforming only the algebra of the Universe volume, searching for alternative formulations able to account for the modified Friedmann equations emerging in Brane Cosmology and Loop Quantum Cosmology. On a pure quantum level, we implement the two approaches through their original setups and reduce the two resulting Wheeler–DeWitt equations to the same morphological structure, showing how the polymer formalism is associated with a bouncing dynamics while in the Generalized Uncertainty Principle case the singularity is still present. The implications of the wavepacket spreading are also discussed in both approaches, outlining that, when the singularity survives, the Planckian era must necessarily be approached by a fully quantum (non-peaked) state of the Universe.

In this paper, using the Lie symmetry method, we obtain the Lie symmetry group of the potential modified Korteweg–de Vries (potential mKdV) equation, and we construct the optimal system of one-dimensional subalgebras for the Lie symmetry algebra of this equation. Furthermore, similarity reductions related to the infinitesimal generators of the Lie symmetry group are obtained. Also, we construct new conservation laws for this equation by the scaling method. This method is algorithmic and based on the linear algebra tools and calculus of variations. The density of the conservation laws is constructed using the Euler operator and scaling symmetry of the equation and also the associated flux is calculated by the homotopy operator. This density-flux pair renders a conservation law for the potential mKdV equation. We specify the density-flux pairs of conservation laws in ranks 4, 8, 12, 16 and 20 for the potential mKdV equation.

In this work, we generalize the constant-roll condition for minimally coupled canonical scalar field inflation. Particularly, we shall assume that the scalar field satisfies the condition $\ddot{\varphi }=\alpha (\varphi )V^{\prime }(\varphi )$, and we derive the field equations under this assumption. We call the framework extended constant-roll framework. Accordingly, we calculate the inflationary indices and the corresponding observational indices of inflation. In order to demonstrate the inflationary viability, we choose three potentials that are problematic in the context of slow-roll dynamics, namely, chaotic, linear power-law and exponential inflation, and by choosing a simple power-law form for the smooth function $\alpha (\varphi )$, we show that in the extended constant-roll framework, the models are compatible with the latest 2018 Planck constraints on inflation. We also justify appropriately why we called this new framework extended constant-roll framework, and we show that the condition $\ddot{\varphi }=\alpha (\varphi )V^{\prime }(\varphi )$ is equivalent to the condition $\ddot{\varphi }=\beta (\varphi )H\dot{\varphi }$, with the latter condition being a simple generalization of the constant-roll condition. Finally, we examine an interesting physical situation, in which a general extended constant-roll scalar field model is required to satisfy the cosmological tracker condition used in quintessence models. In contrast to the slow-roll and ordinary constant-roll cases, in which case the tracker condition is not compatible with neither the slow-roll or the ordinary constant-roll conditions, the extended constant-roll condition can be compatible with the tracker condition. This feature leads to a new inflationary phenomenological framework, the essential features of which we develop in brief. The main feature of the new theoretical framework is that the function $\alpha (\varphi )$ and the potential $V(\varphi )$ are no longer free to choose, but these are directly functionally related.

The current study examines the geometry of static wormholes with anisotropic matter distribution in the context of modified $f({𝒢})$ gravity. We consider the well-known Noether and conformal symmetries, which help in investigating wormholes in $f({𝒢})$ gravity. For this purpose, we develop symmetry generators associated with conserved quantities by taking into consideration the $f({𝒢})$ gravity model. Moreover, we use the conservation relationship gained from the classical Noether method and conformal Killing symmetries to develop the metric potential. These symmetries provide a strong mathematical background to investigate wormhole solutions by incorporating some suitable initial conditions. The obtained conserved quantity performs a significant role in defining the essential physical characteristics of the shape-function and energy conditions. Further, we also describe the stability of obtained wormholes solutions by employing the equilibrium condition in modified $f({𝒢})$ gravity. It is observed from graphical representation of obtained wormhole solutions that Noether and conformal Killing symmetries provide the results with physically accepted patterns.

This paper is devoted to explore some interesting wormhole solutions for the Rastall teleparallel gravity. To complete this analysis, we consider the traceless energy–momentum tensor taken with the Casimir effect concept. Further, we develop two different relations between the pressure components. The anisotropic source of matter with the spherically symmetric space-time is taken to calculate the exact solution, as the shape function. The field equations for Rastall teleparallel gravity are calculated. All the energy conditions are presented for Rastall teleparallel gravity. The presence of exotic matter is confirmed via the violation of energy conditions. All the necessary properties for shape function in all cases are presented graphically. All the inquired results are concluded.

It is generally remarkable to discuss black hole thermodynamics by considering the phenomenon of phase transition for a most general class of static spacetime. For this purpose, we consider the charged Newman–Unti–Tamburino accelerating and rotating pair of black holes. Then, we check the validation of the first law of thermodynamics as well as calculated some thermodynamic quantities like Bekenstein–Hawking entropy area relationship, specific heat, effective temperature, and effective pressure at critical points. We also examine the physical behavior of such thermodynamic potentials and check the global and local stability with the help of Gibbs free energy and specific heat. Moreover, we investigate the difference in the behavior of phase transition for acceleration horizons, inner and outer horizons. Finally, using Ehrenfest’s equations, we describe the existence of phase transition by Prigogine–Defay ratio at the critical points.

Starting with the quaternionic Minkowski space–time and its four-vector representation, a rotational analogue of the quaternionic Dirac equation in the electromagnetic field is developed, which includes not only the energy solutions but also the angular momentum solutions for rotating Dirac fermions. The striking feature of the quaternionic approach is that it depicts a unified representation of energy–momentum in a single framework as the space–time. Furthermore, we establish the generalized Schrodinger–Pauli-like equation associated with generalized electric and magnetic dipole energies that corresponds to their dipole moments. As such, the present analysis deals with the invariant behavior of the extended quaternionic rotational Dirac equation under Lorentz–Poincaré, Gauge, duality, and CPT invariance.

The purpose of our work is to investigate some new features of a static anisotropic relativistic hybrid compact star composed of strange quark matter (SQM) in the inner core and normal baryonic matter distribution in the crust. Here we apply the simplest form of the phenomenological MIT bag model equation of state $p_q=\frac{1}{3}({\rho }_q-4B_g)$ to correlate the density and pressure of strange quark matter within the stellar interior, whereas radial pressure and matter density due to baryonic matter are connected by the simple linear equation of state $p_r=\alpha \rho -\beta$. In order to obtain the solution of the Einstein field equations, we have used the Tolman–Kuchowicz ansatz [R. C. Tolman, Static solutions of Einstein’s field equations for spheres of fluid, Phys. Rev. 55 (1939) 364–373; B. Kuchowicz, Acta Phys. Pol. 33 (1968) 541] and further derivation of the arbitrary constants from some physical conditions. Here, we examine our proposed model graphically and analytically in detail for physically plausible conditions. In particular, for this investigation, we have reported on the compact object Her $X-1$ [$\mathrm{\text{Mass}}=(0.98\pm 0.12)M_{\odot }$; $\mathrm{\text{Radius}}=8.1_{-0.41}^{+0.41}$ km] in our paper as a strange quark star candidate. In order to check the physical validity and stability of our suggested model, we have performed various physical tests both analytically and graphically, namely, dynamical equilibrium of applied forces, energy conditions, compactness factor and surface redshift. Finally, we have found that our present model meets all the necessary physical requirements for a realistic model and can be studied for strange quark stars (SQS).

The aim of this paper is to formulate a new class of uncertainty principles for the classical Gabor transform in $L^2({ℝ}^d)$. To begin with, we formulate a couple of concentration-based uncertainty principles, including the Benedick–Amrein–Berthier and the local-type uncertainty inequalities for the Gabor transform. Second, we derive several unique weighted uncertainty inequalities, such as the Pitt’s and Beckner’s inequalities for the Gabor transforms on ${ℝ}^d$. Besides, the logarithmic Sobolev-type principles for the Gabor transforms are established at the end.

In this paper, we have generalized the behaviors of transit cosmological model under the observational data with Barrow holographic dark energy. We consider the scale factor field as $\varphi ={\varphi }_0{(t^{\beta }{e}^{\alpha t})}^m$ to get exact solutions for the field equations in a non-flat FRW universe in Brans–Dicke theory. The values of the model parameters $\alpha$ and $\beta$ are obtained by best fitting of 46 observational Hubble data (OHD) points in the range $0\le z\le 2.36$. The derived model exhibits a transition scenario for open, flat and closed universe. The EoS parameter shows a quintom-like behavior, lies both quintessence ($\omega >-1$) and phantom ($\omega <-1$) regions and crosses the phantom divide. The matter and dark energy density parameters $({\rho }_D,{\rho }_m)$, scalar field $\varphi$ and other cosmological parameters provide the results consistent with the recent observational datasets. Some other physical and geometrical behaviors of BHDE are also described and the satisfactory behaviors are found with current observations (OHD+JLA).

In this paper, we investigate the behavior of cosmologies in homogeneous and isotropic background with a barotropic fluid. We solve the continuity equation and study several aspects of model including behavior of cosmological quantities like Hubble parameter, deceleration parameter, equation of state parameter along with statefinder diagnostic and validity of energy conditions. The ${\gamma }^{\prime }-\gamma$ plane is checked for identification of thawing and freezing regions. We derive the Lagrangian formulation with standard and non-standard kinetic terms for barotropic fluid model. It is demonstrated that the model possesses periodic potential in its Lagrangian description with standard kinetic terms. Using dynamical system analysis, we find the stability of solutions, too. We further explore the thermodynamic aspects at apparent horizon by investigating the validity of generalized second law of thermodynamics with equilibrium description. The model exhibits complete cosmological scenario for different values of model parameters and the inflationary scenario decays smoothly into radiation-dominated phase during its evolution. The model approaches to $\mathrm{\Lambda }$ cold dark matter model during late times of its evolution.

The simplest, i.e. the Abelian, i.e. the commutative, i.e. the integrable, i.e. the flat and torsion-free, i.e. the symmetric teleparallel affine connection has been considered in many recent works in the literature. Such an affine connection is characterized by the property that it can be vanished by a general coordinate transformation, by fixing the so-called coincident gauge. This paper focuses on the subtleties involved in the applications of the coincident gauge.

In this paper, we obtain an exact spherically symmetric wormhole solution with anisotropic matter distribution in the regularized four-dimensional (4D) Einstein Gauss–Bonnet gravity (4D EGB). Recently, a new attempt has been made to include nontrivial contributions of Gauss–Bonnet term to the gravitational dynamics by regularizing EGB gravity in $4$-dimensions. To find the exact solution of the wormhole geometry, we studied two specific radial-dependent shape functions $b(r)=r_0{(\frac{cosh(r_0)}{cosh(r)})}^{\mu }$, $0<\mu <1$ and $b(r)=r_0(\frac{a^r}{a^{r_0}})$, $0<a<1$ in the context of 4D EGB gravity. For each shape function, we find the exact wormhole solution and analyze the properties of wormhole existence graphically. The anisotropic parameter, equation of state (EoS) and energy conditions are tested graphically for each shape function. The behavior of both shape functions is thoroughly evaluated with the throat radius $r=r_0=1$. Specifically, we recovered the original results exactly to 4D Morris–Throne wormholes of General Relativity by simply imposing the limit as $\alpha \to 0$ and comparison has been done between the branch results in 4D EGB gravity and General Relativity by graphical point of view.

In this paper, geometrical interpretation of the Timoshenko–Ehrenfest theorem is given. It is based on a vector-valued version of continuum mechanics, which considers the deformed body as a surface in extended coordinate space. Scalar parameters of the metrics of this hypersurface determine the strain. In the bending beam case, this surface is formed by a twisted cylinder rolled into a cone. Accordingly, three kinds of metric parameters, the stretch ratio, the twist and cone angles responsible for stretching, shear, and bending determine the shape of the elastic curve. The balance equations for generalized forces taking into account shear deformation and rotational bending effects are derived. A new formula for the shear coefficient comes out of the derivation. It is shown that its magnitude 5/6 for quasistatic Timoshenko beam remains fair for the exact form of the cross-section at the free end.

In this paper, we prove that the gravity theory based on a generalized Lagrangian density, which depends in a nonlinear way not only upon the entire curvature tensor, but also upon its covariant derivatives up to a fixed order $n$, is equivalent to the standard Einstein theory of gravitational field, maybe interacting with additional matter fields.