In this paper, we derive the Darboux solutions of Ito-type coupled KdV equation in Darboux framework which is associated with Hirota Satsuma systems. One of the main results is the generalization of Nth-fold Darboux solutions in terms of Wronskians. We also derive the exact multi-soliton solutions for the coupled field variables of that system in the background of zero seed solutions. With the addition

In previous works, we have proven that there are local tetrads in four-dimensional curved Lorentzian spacetimes that can be written in terms of two kinds of local structures, the skeletons and the gauge vectors. These tetrads diagonalize locally and covariantly the stress–energy tensors for systems of differential equations of the Einstein–Maxwell kind in the Abelian electromagnetic case, or of the

In this paper, we study a class of conformal metric deformations in the quasi-radial coordinate parametrizing the three-sphere in the conformally compactified Minkowski spacetime S1×S3. Prior to reduction of the associated Laplace–Beltrami operators to a Schrödinger form, a corresponding class of exactly solvable potentials (each one containing a scalar and a gradient term) is found. In particular

This study investigated the formation and evolution of a strange star known as SAX.J1808.4–3658 in the Krori–Barua Rainbow spacetime, resulting from the collapse of string fluid. The study examined the dynamical variables derived from the field equations, taking into consideration the influence of the particle’s energy on the mass density, pressure, and string tension. Additionally, various techniques

Wormholes are considered both from the Wheeler deWitt equation, as well as from the field equations in the Euclidean background of Robertson Walker mini-superspace in R2 gravity. Quantum wormhole satisfies Hawking Page wormhole boundary condition in the Euclidean background of mini-superspace, however, in the Lorentzian background wave functional turns to the usual oscillatory function. The Euclidean

This paper aims to provide a consistent, finite-valued, and mathematically well-defined reformulation of Feynman’s path-integral measure for quantum fields obtained by studying the Wiener stochastic process in the infinite-dimensional Hilbert space of quantum states. This reformulation will undoubtedly have a crucial role in formulating quantum gravity within a mathematically well-defined framework

This research investigates the impact of modified gravity on cosmic scales, focusing on f(Q) cosmology. By applying energy conditions, the study reconstructs various f(Q) models, considering an accelerating Universe, quintessence, and a cosmological constant Λ. Using up-to-date observational data, including the Supernova Pantheon sample and cosmic chronometer data, Hubble constants H0 are estimated

In this paper, we establish a generalized Wintgen inequality for quaternionic bi-slant submanifolds and QR-submanifolds (with minimal codimension) in quaternion space forms. We also aim to characterize the second fundamental form of those submanifolds for which the equality cases can hold. Finally, we provide examples of submanifolds embedded in quaternion space forms to support our results.

By the Hirota bilinear method, some new interaction solutions with the complex perturbation for CDGKS equation are obtained. Meanwhile, with the help of the classical nonlinear KdV equation, many new exact solutions of CDGKS equation are derived through the CKdVE method, since it satisfies the CKdVE solvability. Two typical examples also show the local geometric characteristics of the parameter perturbation

We proceed to obtain an exact analytical solution of the Brans–Dicke (BD) equations for the spatially flat (k=0) Friedmann–Lamaître–Robertson–Walker (FLRW) cosmological model in both cases of the absence and presence of the cosmological constant. The solution method that we use to solve the field equations of the BD equations is called the “invariants of symmetry groups method” (ISG method). This method

This paper is devoted to observe the physical attributes of static spherically symmetric isotropic compact stellar candidates in the context of Rastall theory of gravity. In order to inspect the structural composition of compact objects, the Heintzmann ansatz is taken into account. The unknown parameters associated with Heintzmann ansatz are evaluated through matching conditions with derived values

In this study, our main focus is to investigate the mass–radius relation and several important properties of massive neutron stars to realize the nature, behavior and evolution of these kinds of compact objects at present time. Also, we want to understand the equation-of-state of the core nuclear matter precisely with their stable equilibrium configuration. We have chosen a few massive binary pulsars

Through this paper, we consider the time-fractional deformed fifth-order Korteweg–de Vries (KdV) equation. First of all, we detect its symmetries by Lie group analysis with the help of Riemann–Liouville (R-L) fractional derivatives. These symmetries are employed to convert the considered equation into a fractional ordinary differential (FOD) equation in the sense of Erdélyi-Kober (E-K) fractional operator

The Korteweg–de Vries (KdV) equation is an essential model to characterize shallow water waves in fluid mechanics. Here, we investigated the generalized time and time-space fractional KdV equation with fractional derivative of Riemann–Liouville. At the beginning of, we applied the fractional Lie symmetry scheme to derive their symmetry, respectively. We found that the vector fields of these considered

The development and stability of acoustic thin-shell wormholes (WHs) within the context of acoustic black holes are examined in this paper. Utilizing linearized radial perturbations, the stability of these WHs is examined. In this study, a variety of equations of state are taken into account, including barotropic, variable Chaplygin, and phantom-like equations of state. According to the findings, the

The new generalized hypergeometric function (Yang 𝕐-function) described by the contour-type Mellin–Barnes integral representation serves as the inspiration for this study. The incomplete Yang 𝕐-functions γ𝕐r,sp,q(z) and Γ𝕐r,sp,q(z) that we shall introduce here are the appropriate extension of a class of 𝕐-functions by merit of the gamma functions of incomplete type, γ(σ,x) and Γ(σ,x). In this

This paper considers the possibility that abstract thinking and advanced synthesis skills might encourage extraterrestrial civilizations to accept communication with mankind on Earth. For this purpose, a notation not relying upon the use of alphabet and numbers is proposed, in order to denote just some basic geometric structures of current physical theories: vector fields, 1-form fields, and tensor

Thermodynamic extrinsic curvature is a new mathematical tool in thermodynamic geometry. By using the thermodynamic extrinsic curvature, one may obtain a more complete geometric representation of the critical phenomena and thermodynamics. We introduce nonperturbative thermodynamic extrinsic curvature of an ideal two-dimensional gas of anyons. Using extrinsic curvature, we find new fixed points in nonperturbative

In this paper, we investigate the scalar field dark energy (DE) models within the context of F(T,TG) gravity. Scalar field models are known for their dynamic nature. Parameters in the dynamical equation of state are responsible for the acceleration of the cosmos in recent epochs. We determined that the power-law cosmology fits the OHD and Pantheon data nicely. Using the Bayesian analysis and likelihood

A new definition of entropy is introduced using a model that simulates an expanding space-time compatible with the fundamental principle of cosmology. The entropy is obtained by mean of a state function that measures the variation of the space-time normal curvature, from a highly compressed space to a lower compressed space. The defined entropy leads to work out a new understanding of the earliest

In this paper, our purpose is to investigate the anisotropic stellar structure caused by f(R,ϕ) modified gravity, where R represents the Ricci scalar and ϕ represents the scalar potential. This study emphasizes the impact of static spherically symmetric stellar structures using anisotropic distribution. Furthermore, an anisotropic matter source is employed to explore the stability of star formations

In this study, the structures of stars are examined using the Karmarkar condition (KC) to assess the metric components. The study also takes into account the anisotropic source of the matter distribution in the context of Modified Teleparallel Rastall Gravity (MTRG). Various values of the model parameter η are tested by assuming different metric coefficients for the embedding spacetime. To calculate

In this paper, we investigate the bouncing behavior of the universe within the framework of f(R,Lm) gravity, using a simple form of f(R,Lm)=R2+Lmγ (where γ is a free model parameter) as previously studied. The model predicts a vanishing Hubble parameter in the early and late times, with the deceleration parameter approaching a specific limit at the bouncing point. The EoS parameter is observed to cross

This study explores the deflection angle of photon rays or light-like geodesics within the framework of Eddington-inspired Born–Infeld (EiBI) gravity background space-time, taking into account the influence of cosmic strings. The primary focus lies in deriving the effective potential of the system applicable to both null and time-like geodesics, as well as determining the angle of deflection for light-like

In this paper, we study the topological effects of the global monopole spacetime on the energy eigenvalues of spherical symmetric potentials in the nonrelativistic regime. We deal with the radial equation by using the Wentzel, Kramers and Brillouim (WKB) approximation. In the cases where the energy levels of the ℓ-waves can be achieved, the WKB approximation is used based on the Langer transformation

In this paper, we have provided a discussion regarding the structural properties of a spherical compact stellar object within the background of f(R,G) modified gravity. We have considered that the interior region of the compact stellar body is filled by a composition of anisotropic dark energy and isotropic normal matter which are assumed to be non-interacting. To relate the two stated fluids, we have

In this study, we investigate the deflection angle of a torus-like regular charged black hole in the limit approximation of a weak field to check the effects of non-magnetic plasma and non-plasma medium. Using spacetime optical geometry, we first compute the Gaussian optical curvature. We study the light deflection angle from a charged torus-like black hole using the Gibbons and Werner approach. By

In this paper, we study Little Rip (LR) and Pseudo Rip (PR) cosmological models containing two coupled fluids: dark energy and dark matter. We assume a spatially flat Friedmann–Robertson–Walker (FRW) universe. The interaction between the dark energy and the dark matter fluid components is described in terms of the parameters in the generalized Equation of State (EoS) in presence of the bulk viscosity

This paper is devoted to N-wave equations with constant boundary conditions related to symplectic Lie algebras. We study the spectral properties of a class of Lax operators L, whose potentials Q(x,t) tend to constants Q± for x→±∞. For special choices of Q±, we outline the spectral properties of L, the direct scattering transform and construct its fundamental analytic solutions. We generalize Wronskian

In this paper, we employ parametrization techniques within the framework of f(T) gravity to investigate the deceleration parameter (DP), a key quantity characterizing the universe’s expansion dynamics. By analyzing the DP, we gain valuable insights into the nature of cosmic constituents and their impact on the universe’s evolution. We utilize a combination of observational data, including 31 Cosmic

We obtained the solutions of Einstein’s Field Equations (EFEs) for locally rotationally symmetric (LRS) Bianchi type-I perfect fluid spacetimes through the concircular vector fields (CCVFs) in f(T) gravity. It is shown that such metrics admit CCVFs of 4, 5, 6, 7, 8 and 15 dimensions. We also calculated the energy density, fluid pressure, torsion scalar T and the form of the function f(T). We did not

In this paper, we explore a set of geometric properties of Mixed Super Quasi-Einstein (MSQE) manifolds and provide examples of both Riemannian and Lorentzian MSQE manifolds to demonstrate their existence. Furthermore, we examine MSQE spacetimes in the context of the space-matter tensor, discussing several related properties. Finally, we establish the existence of an MSQE spacetime through a nontrivial

In this paper, we aim to characterize the sequential warped product κ-almost gradient conformal Ricci–Bourguignon soliton. We derive applications of some vector fields like conformal vector field, torse-forming vector field, torqued vector field on κ-almost conformal Ricci–Bourguignon soliton. The inheritance properties of the Einstein-like sequential warped product κ-almost gradient conformal Ricci–Bourguignon

In this paper, we will discuss an alternative theory for the origin of dark matter and dark energy based on the new concept of tetrad gauge states of spacetime. The new tetrads already introduced new physics since it has been proved that local electromagnetic gauge transformations can boost the local tetrad fields in a four-dimensional curved Lorentz spacetime. It is within this context that we will

In this paper, a class of anisotropic compact stars is analyzed in Heintzmann geometry. The Einstein field equations (EFEs) have been solved to obtain the stellar model in presence of pressure anisotropy. We have considered the gtt metric component as proposed by Heintzmann, and by solving the EFEs, the grr metric component is evaluated in the presence of pressure anisotropy. It is noted that for an

For vector nonlocal reverse-space nonlinear Schrödinger equations, a binary Darboux transformation is formulated by using two sets of eigenfunctions and adjoint eigenfunctions. The resulting binary Darboux transformation has been decomposed into an N-fold product of single binary Darboux transformations. An application starting from zero seed potentials generates a class of soliton solutions.

In this paper, we explore the characteristics of two novel regular spacetimes that exhibit a nonzero vacuum energy term, under the form of a (quasi) anti-de Sitter phase. Specifically, the first metric is spherical, while the second, derived by applying the generalized Newman–Janis algorithm to the first, is axisymmetric. We show that the equations of state of the effective fluids associated with the

In this paper, our aim is to research the change in the magnetic field using the curvature theory of ruled surfaces. For this, we examine magnetic curves of the curve whose existence is guaranteed from the derivative formulas of the rotation frame. The Killing vector fields and Lorentz forces of these magnetic curves are calculated. Additionally, correlations between curvatures are obtained. Flux ruled

The optical and geometric properties of a class of generalized conics are presented. The study makes it possible to find in an original way several results of classical geometry and to connect numerous curves by a common law. Applications in geometric optics are envisaged, with the production of diopters, lenses or mirrors.

This research paper explores the properties of quasi-Einstein manifolds with a unit concircular generator vector field within doubly warped product structures. The paper begins by investigating the characteristics of quasi-Einstein manifolds that possess a unit concircular generator vector field. Subsequently, it analyzes the behavior of the Hessian, Riemann, and Ricci vector fields in the context

In this review, we provide a concrete overview of the Raychaudhuri equation, Focusing Theorem and convergence conditions in a plethora of backgrounds and discuss the consequences. We also present various classical and quantum approaches suggested in the literature that could potentially mitigate the initial big-bang singularity and the black-hole singularity.

In this paper, we review a recently offered notion of quasi-static evolution of the axial self-gravitating structures at large scales and the criterium to characterize the corresponding evolutionary aspects under the influence of strong curvature regimes. In doing so, we examine the axial source’s dynamic and quasi-static behavior within the parameters of various modified gravity theories. We address

The purpose of this paper is to investigate the existence of Ricci solitons and the nature of curvature inheritance as well as collineations on the Robinson–Trautman (briefly, RT) spacetime. It is shown that under certain conditions RT spacetime admits almost-Ricci soliton, almost-η-Ricci soliton, almost-gradient η-Ricci soliton. As a generalization of curvature inheritance [K. L. Duggal, Curvature

The center of this paper is to establish the generalized variational structure (GVS) of the (3+1)-dimensional Zakharov–Kuznetsov–Burgers equation (ZKBe) by taking advantage of the Semi-inverse method (SIM). Two different GVSs are extracted and the derivation process is presented in detail. The extracted GVSs reveal the energy conservation law and can offer some new insights on the study of the variational

In this paper, we analyze energy density inhomogeneities for charged fluid configuration in the background of f(T) theory and recognize its prime features as computed in GR. The dynamical equations are composed employing Bianchi identities for the standard, f(T) extra terms, and energy-momentum tensor for the electromagnetic field. We evaluate various mathematical models of dissipative and anisotropic

In this paper, we investigate the geometric phase (GP) of two-mode entangled squeezed-coherent states (ESCSs), undergoing unitary cyclic evolution. Results show that increasing the squeezing parameter of either mode of the balanced ESCS compresses the GP elliptically with respect to the coherence parameter of the corresponding mode. While in the case of unbalanced ESCS, the GP is compressed hyperbolically

In the recently suggested modified non-metricity gravity theory with boundary term in a flat FLRW spacetime universe, dark energy scenarios of cosmological models are examined in this study. An arbitrary function, f(Q,C)=Q+αC2, has been taken into consideration, where Q is the non-metricity scalar, C is the boundary term denoted by C=R̈−Q, and α is the model parameter, for the action that is quadratic

In this paper, we investigate the bouncing universe in a modified gravity model f(Q,T). The bouncing universe theory posits that the universe goes through periodic expansions and contractions, with a “bounce” occurring at the end of each contraction that leads to a new expansion. This theory suggests that our universe didn’t emerge on its own out of nothing, but is instead the latest in a series of

In this paper, we obtain a Lichnerowicz-type formula for J-Witten deformation and give the proof of the Kastler–Kalau–Walze-type theorems associated with J-Witten deformation on four-dimensional and six-dimensional almost product Riemannian manifold with (respectively, without) boundary. We give an explanation of the Einstein–Hilbert action for J-Witten deformation on four-dimensional manifold with

In this work, we reconsider the study of black holes and black strings in the compactification of M-theory on a Calabi–Yau three-fold, considered as a complete intersection of hypersurfaces in a product of weighted projective spaces given by 𝕎ℙ4(ω,1,1,1,1)×ℙ1. Using the N=2 supergravity formalism in five dimensions, we examine the BPS and non-BPS solutions by wrapping M-branes on appropriate cycles

The goal of this paper is to analyze sharp-type inequalities including the scalar and Ricci curvatures of bi-slant Riemannian submersions in complex space forms. Then, for bi-slant Riemannian submersion between a complex space form and a Riemannian manifold, we give inequalities involving the Casorati curvature of the space ker φ∗. Also, we mention some examples.

In this paper, we have computed the spectrum and the q-index of the super q-deformed Ginsparg–Wilson Dirac operator in the different cases (fuzzy, non-fuzzy, gauged, and non-gauged) on the superquantum fuzzy two-sphere Sqμ(2|2). We also presented the appropriate spin structure that this operator acts on the superquantum (Dirac) spinor bundle. Finally, it was shown that in the non-quantum limit, when

Monounary algebras are the most simple type of an algebraic structure. Oriented graphs with one outgoing arrow from every vertex represent them. The aim of this paper is to point out the interdisciplinary relationships concerning this structure. Bernoulli shift is a paradigmatic mapping in dynamical systems. It is also called dyadic, bit shift, doubling or sawtooth. We offer a look at the properties

We review Holst formalism and dynamical equivalence with standard GR (in dimension 4). Holst formalism is written for a spin coframe field eμI and a Spin(3,1)-connection ωμIJ on spacetime M and it depends on the Holst parameterγ∈ℝ−{0}. We show the model is dynamically equivalent to standard GR, in the sense that up to a pointwise Spin(3,1)-gauge transformation acting on (uppercase Latin) frame indices

Dabrowski et al. [Spectral metric and Einstein functionals for Hodge–Dirac operator, preprint (2023), arXiv:2307.14877] gave spectral Einstein bilinear functionals of differential forms for the Hodge–Dirac operator d+δ on an oriented even-dimensional Riemannian manifold. In this paper, we generalize the results of Dabrowski et al. to the cases of 4-dimensional oriented Riemannian manifolds with boundary

We review some recent results on the mathematical foundations of a quantum theory over a scalar field that is a quadratic extension of the non-Archimedean field of p-adic numbers. In our approach, we are inspired by the idea — first postulated in [I. V. Volovich, p-adic string, Class. Quantum Grav.4 (1987) L83–L87] — that space, below a suitably small scale, does not behave as a continuum and, accordingly

In this paper, we study the tunneling radiation from a charged-accelerating AdS black hole with gauge potential under the impact of quantum gravity. Using the semi-classical phenomenon known as the Hamilton–Jacobi ansatz, it is studied that tunneling radiation occurs via the horizon of a black hole and also employs the Lagrangian equation using the generalized uncertainty principle. Furthermore, we

In this paper, we present a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by state vectors evolving under nonstationary Hamiltonians. Specifically, relying on the existing geometric viewpoint for stationary Hamiltonians, we discuss the generalization of our theoretical construct to time-dependent quantum-mechanical scenarios where both time-varying curvature

We develop a notion of causal order on a generic manifold as independent of the underlying differential and topological structure. We show that sufficiently regular causal orders can be recovered from a distinguished algebra of sets, which plays a role analogous to that of topologies and σ algebras. We then discuss how a natural notion of measure can be associated to the algebra of causal sets.

This investigation employs advanced computational techniques to ascertain novel and precise solitary wave solutions of the Camassa–Holm (𝒞ℋ) equation, a partial differential equation governing wave phenomena in one-dimensional media. Originally designed for the representation of shallow water waves, the 𝒞ℋ equation has exhibited versatility across various disciplines, including nonlinear optics and