International Journal of Geometric Methods in Modern Physics

This work provides the exact solution of the Bardeen black hole in association with $4D$ Gauss–Bonnet massive gravity in Anti-de-Sitter $(AdS)$ space–time. It is a modification of the Gauss–Bonnet when gravity couples with nonlinear matter fields which is the function of the electromagnetic field. The obtained solution gives rise to $4D$ EGB Bardeen black holes when the massive gravity parameter is set to zero and it yields a $4D$ Gauss–Bonnet black hole in the absence of magnetic monopole charge. Further, we analyze and adopt the thermodynamic quantities like mass ($M_{+}$), temperature $(T_{+})$ and heat capacity $(C_{+})$ in the presence of massive gravity and nonlinear electrodynamics. In addition, we extend our results by considering the cosmological constant $(\mathrm{\Lambda })$ as a thermodynamical variable $(P=-\mathrm{\Lambda }/8\pi )$ and obtain the critical values of pressure, temperature, horizon radius and analyze the behavior of the global parameter $P_c{v}_c/T_c$. The effect of a massive parameter ($m$) of the critical exponent is opposite to the magnetic monopole charge ($e$) and Gauss–Bonnet parameter ($\alpha$). According to our analysis the phase transition between a small and large black hole and van der Waals phase transition are analogous to each other.

In this paper, we investigated the general behaviors of the Tsallic holographic dark energy (THDE) model in general relativity. Here, we take the Bianchi $V{I}_0$ metric, which is homogeneous and anisotropic. We investigate the THDE models with the Hubble horizon and Granda–Oliveros (GO) cutoffs. We have studied the behavior of a few quantities, such as dark energy density $({\rho }_D,)$, matter-energy density $({\rho }_m)$, and skewness parameter $(\gamma )$ and discuss their physical significances. In our THDE models, the EoS parameter explains the universe’s evolution based on the value of the non-extensive or Tsallis parameter $\delta$. In addition, we develop the cosmographic parameters like, deceleration parameter $(q)$, jerk parameter $(j)$, lerk parameter $(l)$, snap parameter $(S)$ and maxout parameter $(m)$. We have explored the ${\omega }_D-{\omega }_D^{\prime }$ plane and the stability analysis of the THDE model by a perturbation method. We have also constructed a correspondence between the THDE model with quintessence. Some physical and geometrical behaviors of the models are also discussed.

In this paper, a generalized Darboux transformation is obtained for Fordy–Kulish NLS (nonlinear Schrödinger) systems on general Hermitian symmetric spaces in order to rigorously obtain rogue wave solutions for these systems. In particular, we express the generalized algebraic relations in a simple and elegant compact form. As an illustration, we derive multi-soliton, breather-type and mainly rogue wave solutions of triangular patterns for single- and multi-component NLS systems on $C{P}^1$ and $SP(2)/U(2),$ respectively. We also analyze the modulation instability of proper plane wave solutions. In order to get visual intuition for the dynamics of the result and solutions for the running examples, the associated simulations of profiles are furnished as well.

This paper is focused on the investigation of wormhole solutions in $f(Q)$ gravity, where $Q$ denotes the non-metricity scalar. To obtain these solutions, three specific forms of $f(Q)$ gravity models are considered and the shape function, which is responsible for the shape of the wormhole, has been obtained numerically for each model. Further, the energy conditions are checked and the stability of solutions is obtained by determining the adiabatic sound speed in each case.

Black hole’s quasinormal frequencies are basically the complex numbers which provide information about the relaxation of perturbations and depend on the characteristics of the spacetime and types of perturbations. In this paper, we evaluate the spectrum of the quasinormal modes of Hayward black hole in Einstein–Gauss–Bonnet gravity, Hayward black hole in anti-de Sitter space (AdS) spacetime, and 4-dimensional black hole in Einstein–Lovelock gravity. By utilizing the 6th-order WKB resonance technique, we examine the quasinormal modes frequencies $\omega$ by shifting the charge parameter $Q$ (it is also identified with the cosmological constant), circular harmonic index $l$, and mass of scalar field $m$. We observe that 6th-order WKB method gives quite high accuracy when the multipole number $l$ is larger than the overtone $n$. We observe that real and imaginary components of the quasinormal modes are not linear functions similar to Reisnner–Nordström-AdS. For large values of charge, quasinormal ringing becomes slower to settle down to thermal equilibrium and hence the frequency of the oscillation becomes smaller.

In this paper, we calculate a new class of wormhole solutions in the framework of teleparallel gravity. To obtain a characteristic wormhole solution, we use anisotropic matter distribution and a specific form of two dark matter profiles (URC profile and Quantum wave dark matter). As a general strategy, we create a relationship between calculated energy density and dark matter profiles for the system and investigate the physical properties of the wormhole geometry. A detailed analytical and graphical explanation of the matter contents via energy conditions is provided. The calculated shape functions of wormhole geometry meet the required conditions in both circumstances. Several intriguing features have emerged from the investigation, as have the properties of the exotic matter within the wormhole geometry. Finally, we have concluding remarks.

In this paper, we investigate the late-time accelerated universe evolution in a flat, homogeneous and isotropic model in the context of $f(Q,T)$ gravity, where $Q$ and $T$ are non-metricity scalar and trace of energy–momentum tensor, respectively. The scale factor, by construction, yields ekpyrotic contraction era followed by a non-singular bounce. The expanding era of the universe yields late-time dark energy era preceded by matter-dominating decelerating era. The model unifies an ekpyrotic, non-singular bounce with the present dark energy-dominated epoch. The model parameters in the functional form of $f(Q,T)$ gravity affect the dynamical evolution of the equation of state (EoS) parameter. The theoretical value of EoS parameter is found to be ${\omega }_0=-1.0136,-1.0273$ for $n=0,1$, respectively, and it lies in range of the estimated value of EoS parameter from the Planck+SNe+BAO observational data. Different aspects of this bouncing model including behavior of geometrical and physical quantities along with energy conditions have been discussed in detail.

We calculate the entanglement entropy between two (maximally-extended) spacetime regions of static black hole, separated by horizon. As a first case, we consider the Schwarzschild black hole, and then we extend the calculations to the charged Reissner–Nordström and Schwarzschild–de Sitter black holes with more than one horizon. The case for static and spherically-symmetric solution to the more general $F(R)$ gravity is also considered. The calculation of the entanglement entropy is performed using the replica trick by obtaining the explicit form of the metric which corresponds to the replica spacetime for each black hole under consideration. The calculation of static and spherically-symmetric black holes results in the entanglement entropy that matches the Bekenstein–Hawking area law entropy.

This paper is devoted to the obtain Chen inequalities containing the Ricci and scalar inequalities on the vertical and the horizontal distributions for semi-slant Riemannian submersions from complex space forms onto Riemannian manifolds. The equality case of the obtained inequalities is discussed. At the end, some geometric consequences are obtained. Moreover, many examples are constructed.

In this paper, we have investigated an anisotropic cosmological model in $f(Q)$ gravity with string fluid in LRS Bianchi type-I universe. We have considered the arbitrary function $f(Q)=Q+\alpha \sqrt{Q}+2\mathrm{\Lambda }$, where $\alpha$ is model free parameter and $\mathrm{\Lambda }$ is the cosmological constant. We have established a relationship between matter energy density parameter ${\mathrm{\Omega }}_m$ and dark energy density parameter ${\mathrm{\Omega }}_{\mathrm{\Lambda }}$ through Hubble function using constant equation of state parameter $\omega$. We have made observational constraint on the model using ${\chi }^2$-test with observed Hubble datasets $H(z)$ and SNe Ia datasets, and obtained the best fit values of cosmological parameters. We have used these best fit values in the result and discussion. We have discussed our result with cosmographic coefficients and found a transit phase dark energy model. Also, we analyzed the Om diagnostic function for anisotropic universe and found that our model is quintessence dark energy model.

In this paper, we characterize the $\eta$-Einstein cosymplectic manifolds with the gradient Einstein solitons and the conformal vector fields. It is proven that if an $\eta$-Einstein cosymplectic manifold $M^{2n+1}$ of dimension $2n+1$ with $n>1$ admits a gradient Einstein soliton, then either $M^{2n+1}$ is Ricci flat or the gradient of Einstein potential function is pointwise collinear with the Reeb vector field of $M^{2n+1}$. Also, we prove that if $M^{2n+1}$ admits a conformal vector field $W$, then either $M^{2n+1}$ is Ricci flat or $W$ is homothetic. We also establish that a conformal vector field $W$ on $M^{2n+1}$ is a strict infinitesimal contact transformation, provided the scalar curvature of $M^{2n+1}$ is constant. Finally, the non-trivial examples of cosymplectic manifolds admitting the gradient Einstein solitons are given.

This paper reflects a study on the thermodynamic features of charged rotating Kerr–Sen–AdS black holes discussed with an extended phase space, where the negative cosmological constant is accounted for pressure. Thermal stability/instability and dependency of the phase transition points on the parameters of a black hole have been discussed further. The authors have systematically studied the throttling process of the black hole considering its mass is identified by its enthalpy. Moreover, the phenomenon of Joule–Thomson expansion has been explored, and inversion temperature for the black hole has been investigated using a numerical approach. Next, a heat engine is constructed by considering the black hole as a working object and subsequently, its efficiency is calculated by considering a rectangular heat cycle in the $P$–$V$ plane. Then the effects of the black hole parameters on its efficiency and their respective roles are studied, followed by a careful comparison of the efficiency with that of a Carnot engine so that the second law of thermodynamics holds true.

The Reynolds Transport Theorem, colloquially known as “differentiation under the integral sign”, is a central tool of applied mathematics, finding application in a variety of disciplines such as fluid dynamics, quantum mechanics, and statistical physics. In this work, we state and prove generalizations thereof to submanifolds with corners evolving in a manifold via the flow of a smooth time-independent or time-dependent vector field. Thereby we close a practically important gap in the mathematical literature, as related works require various “boundedness conditions” on domain or integrand that are cumbersome to satisfy in common modeling situations. By considering manifolds with corners, a generalization of manifolds and manifolds with boundary, this work constitutes a step towards a unified treatment of classical integral theorems for the “unbounded case” for which the boundary of the evolving set can exhibit some irregularity.

We study the variational problem of finding the fastest path between two points that belong to different anisotropic media, each with a prescribed speed profile and a common interface. The optimal curves are Finsler geodesics that are refracted — broken — as they pass through the interface, due to the discontinuity of their velocities. This “breaking” must satisfy a specific condition in terms of the Finsler metrics defined by the speed profiles, thus establishing the generalized Snell’s law. In the same way, optimal paths bouncing off the interface — without crossing into the second domain — provide the generalized law of reflection. The classical Snell’s and reflection laws are recovered in this setting when the velocities are isotropic. If one considers a wave that propagates in all directions from a given ignition point, the trajectories that globally minimize the traveltime generate the wavefront at each instant of time. We study in detail the global properties of such wavefronts in the Euclidean plane with anisotropic speed profiles. Like the individual rays, they break when they encounter the discontinuity interface. But they are also broken due to the formation of cut loci — stemming from the self-intersection of the wavefronts — which typically appear when they approach a high-speed profile domain from a low-speed profile.

In order to analyze Barrow holographic dark energy (BHDE) in a flat FRW universe, the time-dependent scale factor $a(t)={[sinh(\alpha t)]}^{\frac{1}{n}}$ is employed. The Hubble horizon as the IR-cutoff is taken to investigate the cosmic consequences. We demonstrate the cosmic transition using the deceleration parameter and equation of state parameter. The characteristics of deceleration parameter for this model correspond well with the latest findings. The equation of state parameter behaves well and does not cross the phantom line. Depending on the values of Barrow exponent ($\mathrm{\Delta }$), our model is entirely quintessence and is eventually moving towards $\mathrm{\Lambda }\text{-CDM}$ model. We plotted the pressure diagram with various Barrow exponent ($\mathrm{\Delta }$) values to demonstrate dark energy dominance. The scalar field and potential that explain the universe’s accelerating expansion are also reconstructed.

It is an undeniable fact that the negative energy source is essential for the stability of traversable wormholes. Recently, it has been shown that the Casimir energy which is the only artificial source of negative energy till date, could source the negative energy to the traversable wormholes as well. In this paper, we explore the possibility of non-exotic traversable wormholes in 4-D EGB gravity. We use the Yukawa–Casimir shape function and investigate the various energy conditions. We observe that for appropriate choices of shape function and the parameters, traversable wormholes with normal matter at throat can be found.

In this study, we consider Born–Infeld-$f(R)$ gravity in which the $f(R)$ term enters directly into the square root in the Palatini formulation. We briefly analyzed this model for an explicit $f(R)$ function which includes positive and negative powers of the curvature scalar. We also show that both the ordinary Born–Infeld-$f(R)$ and this modification reduce to the same gravitational action form under the conformal approach. Then, we consider the existence of a maximally symmetric vacuum solution for the gravitational field equations and find the de Sitter solution for this modified model.

In this paper, we present a static solution for the five-dimensional Einstein–Gauss–Bonnet (EGB) gravitational field equations with a cylindrical symmetry and an anisotropic fluid as a source. We consider whole set of equations in the interior space which sourced by static cylindrical anisotropic fluid and junction conditions required for smoothly matching with exterior space which is a cylindrical vacuum solution of five dimensional EGB equation. We achieve density and pressures as functions of cylindrical radial coordinate and give some graphically analysis under numerical solution.