Lanczos Equations Research Articles

Exploring thin-shell dynamics in regular charged black hole through T-duality

We present a thin-shell in the background of a regular charged static black hole solution in the presence of T-duality effects for the Einstein–Maxwell system. The thin-shell are developed by matching the inner and outer manifolds through the well-known Visser’s cut-and-paste approach. We produce three types of thin-shells with an outer regular charged black hole from T-duality and different choices of inner manifolds named: 1. Thin-shell (inner flat spacetime), 2. Thin-shell Garvastars (inner de Sitter spacetime), and 3. Thin-shell wormholes (inner regular charged black hole from T-duality) We evaluate the surface stresses of a thin layer of matter contents at a thin-shell through Lanczos equations and also develop equations of motion of these constructed configurations. We also explore thin-shell stability through linearized radial perturbations at equilibrium shell radius with barotropic and generalized Chaplygin equations of state. We show that the stability of respective configurations enhances in the presence of exterior charged BH from T-duality. We conclude that thin-shell Garvastars are more stable than thin-shell and thin-shell wormholes.

New gravastar model in generalised cylindrically symmetric space–time and prediction of mass limit

We present a class of new Gravastar solutions following the works of Mazur and Mottola for a Gravitational Bose–Einstein Condensate (GBEC) star in generalised cylindrically symmetric space–time. A stable gravastar consists of 3 distinct regions, namely: (i) an interior de-Sitter space (p=−ρ), which exerts an outwards repulsive force at all points on the thin shell, (ii) an intermediate thin shell with a slice of finite length separating the interior and exterior regions is supposed to be consisting of an ultra-relativistic stiff fluid, with the equation of state p=ρ and (iii) an exterior vacuum region. This thin shell, which is considered as the critical surface for the quantum phase transition, replaces both the classical de-Sitter space and Schwarzschild event horizon. The new solutions are free from any singularities. The energy density, total energy, proper length, and the entropy of this shell are explored in this model. From the thin shell solution and using Lanczos equations for stress energy density, we have predicted the mass contained into the gravastar shell. The stability of the gravastar model is analysed through the consideration of gravitational surface redshift and entropy calculation. We have also obtained a constraint on the possible mass of the thin shell without violating the condition for stable gravastar configuration. All these features indicate that the present model is physically viable.

Testing of [formula omitted]-gravity through gravastar configurations

In this article, we are reporting for the first time the existence of gravastar configurations in the framework of κ(R,T)-gravity, which can be treated as an alternative to a black hole (Mazur and Mottola). This strengthens how much this new gravity theory may be physically demanding to the gravity community in the near future. We first develop the gravastar field equations for a generic κ(R,T) functional and then we study four different models within this theory. We find that the solutions for the interior region are regular everywhere regardless of the exact form of the κ(R,T) functional. The solutions for the shell region indicate that two of the four models subjected to the study are physically feasible. In addition, the junction conditions are considered at each interface by using the Lanczos equations that yield the surface density and pressure at the thin shell. We investigate various characteristics of the gravastar structure such as the proper length, energy, and entropy of the spherical distribution.

Hyperbolic reduction of the Weyl–Lanczos equations

We provide a new framework to find the Lanczos potential of the Weyl tensor in terms of two symmetric and spatial fields. We show that given any space time with the Einstein field equations coupled to a general matter source, a Lanczos potential can be identified by solving a symmetric hyperbolic system of evolution equations.

Thin-shell wormholes with electromagnetic effects in f(R,T) gravity

The purpose of this paper is to study the feasibility and the appearance of charged thin-shell wormholes using generalized Chaplygin gas under the influence of minimally coupled [Formula: see text] gravitational theory. Here, [Formula: see text] is a generic function of the scalar curvature [Formula: see text] and the trace of stress-energy tensor [Formula: see text]. We explore different components of Lanczos equations in the context of a specific [Formula: see text] functional form, i.e. [Formula: see text], by applying junction conditions on field equations. We study static stable solutions using radial perturbation and the generalized Chaplygin gas equation of state (EoS) with the isotropic environment. We investigate the stable (unstable) static wormhole solutions for various physical parametric values and illustrate them graphically.

Static cylindrically symmetric wormhole models in [formula omitted] gravity

In this manuscript, we will examine thin-shell wormholes in the framework of f(R,T) theory. In this gravitational theory, f is a function of Ricci scalar invariant R and the trace of the stress–energy tensor T. Also, wormholes that appeared as special solutions to Einstein’s field equations, are now being tackled in a variety of ways and are being viewed as viable interstellar objects. By selecting a minimally coupled f(R,T) function, we will reduce modified field equations to their corresponding Lanczos equations. The junction conditions are also manipulated and the generalized Chaplygin gas (GCG) is used to find exact solutions for traversable wormholes. We investigate the stability of these wormholes when they are perturbed while maintaining their symmetry. From the comparison of the obtained graphical solutions, it is found that only unstable solutions to thin-shell wormholes exist.

Gravastars in energy–momentum squared gravity

This paper is devoted to studying the structure of gravitationally vacuum condensate stars under the influence of matter and geometry coupled gravity. This alternative to black hole comprises three domains, i.e. interior, exterior and thin-shell. We investigate such regions by considering particular equations of state for a specific model of energy–momentum squared gravity. The nonsingular solutions of field equations are obtained to describe the interior region of gravastar and the Schwarzschild spacetime represents the exterior region. The junction conditions are used to match interior and exterior domains while Lanczos equations provide the surface density and pressure at thin-shell. We investigate various attributes of gravastar such as the equation of state parameter, entropy, proper length as well as energy. The physical features of a gravitationally vacuum star indicate a linear relationship with the thickness of the shell and provide a viable structure similar to general relativity.

Stability and Dynamics of Regular Thin-Shell Gravastars

This paper explores the stable and dynamical configuration of thin-shell gravastars developed from the matching of exterior (Hayward and Hayward anti-de Sitter black holes) and interior (de Sitter) spacetimes. These spacetimes are connected at a thin-shell by considering Visser cut and paste technique. The matter surface energy density and pressure are formulated from the Lanczos equations. We consider the shaded regions to discuss the stability of gravastars by using radial perturbation at the equilibrium shell radius. We then observe thin-shell dynamics with massless as well as massive scalar field through equations of motion and Klein-Gordon equations. The respective scalar thin-shell represents collapse and expansion of the developed structure with the shell radius, velocity and effective potential. We conclude that stable regions of gravastar shell decrease and dynamical configuration (collapse and expansion) increase with cosmological constant.

Stability of ABG thin-shell around a traversable wormhole

This paper investigates stability of thin-shell developed from the matching of interior traversable wormhole with exterior Ayon–Beato–Garcia–de Sitter regular black hole through cut and paste approach. We employ Israel formalism and Lanczos equations to obtain the components of surface stress-energy tensor at thin-shell. These surface stresses violate null and weak energy conditions that suggest the presence of exotic matter at thin-shell. The surface pressure explains collapse as well as expanding behavior of the developed geometry. We explore stability of the constructed thin-shell through both perturbations along shell radius as well as barotropic equation of state for three appropriate values of the shape function [Formula: see text]. It is concluded that stability of thin-shell depends on the shape function, charge and cosmological constant.

Mechanical stability of a class of regular thin-shell wormholes

This paper explores the stable configuration of thin-shell wormholes constructed from two regular black holes (modified Hayward and four parametric) by using Visser cut and paste approach. The components of stress-energy tensor are evaluated through the Lanczos equations. We analyze the stability of thin-shell by using radial perturbation preserving its symmetries about equilibrium static solution. It is found that modified Hayward wormholes are more stable than the Hayward wormholes. Further, the stable regions of four parametric regular wormholes are larger than the Schwarzschild, Reissner–Nordström and Ayón–Beato–García wormholes. We conclude that stable region decreases for highly charged thin-shell wormholes.

Thin-shell wormholes in Rastall gravity

We constructed thin-shell wormholes using the well-known "cut and paste" technique for static black holes sourced by an anisotropic fluid within the context of the Rastall gravity. Using the generalized Lanczos equations we explored the energy conditions at the wormhole's throat along with the traversability condition. We determined the stability regions when the wormhole configurations are surrounded by different bulk sources and obtained that the stability regions are considerably modified due to the non-trivial dependence of the Rastall parameter in the effective potential energy.

Dynamics of the scalar shell in higher dimensions

This paper investigates the dynamical evolution of thin-shell developed from a class of d-dimensional black holes. The components of stress–energy tensor of surface matter at thin-shell are evaluated through the Lanczos equations. The corresponding equations of motion and effective potential describe the expansion, collapse and saddle points. It is found that expanding and collapsing characteristics of the shell are enhanced for higher-dimensional spacetimes. We also investigate the dynamics of thin-shell in the presence of massless and massive scalar fields. The evolutionary behavior of massless scalar shell is greatly affected by the black hole parameters. The massive scalar field indicates the oscillation of thin-shell for d=5 with specific values of the parameters. This scalar shell shows collapse for higher-dimensional Schwarzschild–de Sitter and quintessence manifolds while it indicates expansion for higher-dimensional Reissner–Nordström black hole.

Influence of nonlinear electrodynamics on stability of thin-shell wormholes

The aim of this paper is to discuss stability of regular thin-shell wormholes coupled with non-linear electrodynamics and cosmological constant. The surface stresses are formulated by using Lanczos equations. We examine attractive and repulsive behavior of these constructed wormholes corresponding to outward and inward-directed acceleration components, respectively. We also investigate stability conditions for the existence of traversable thin-shell wormholes with arbitrarily small amount of different fluids as exotic matter. We consider linear, logarithmic and Chaplygin gas models and find that a modified generalized Chaplygin gas model provides maximum viable regions for stability of the respective thin-shell wormholes. It is found that formation of stable regions for ABGB thin-shell wormholes highly depends on the physically acceptable range of charge and other parameters.

THE HIERARCHY PROBLEM, RADION MASS, LOCALIZATION OF GRAVITY AND 4D EFFECTIVE NEWTONIAN POTENTIAL IN STRING THEORY ON S1/Z2

In this paper, we present a systematical study of braneworlds of string theory on S1/Z2. In particular, starting with the toroidal compactification of the Neveu–Schwarz/Neveu–Schwarz sector in D + d dimensions, we first obtain an effective D-dimensional action, and then compactify one of the D - 1 spatial dimensions by introducing two orbifold branes as its boundaries. We divide the whole set of the gravitational and matter field equations into two groups, one holds outside the two branes, and the other holds on them. By combining the Gauss–Codacci and Lanczos equations, we write down explicitly the general gravitational field equations on each of the two branes, while using distribution theory we express the matter field equations on the branes in terms of the discontinuities of the first derivatives of the matter fields. Afterwards, we address three important issues: (i) the hierarchy problem; (ii) the radion mass; and (iii) the localization of gravity, the four-dimensional Newtonian effective potential and the Yukawa corrections due to the gravitational high-order Kaluza–Klein (KK) modes. The mechanism of solving the hierarchy problem is essentially the combination of the large extra dimension and warped factor mechanisms together with the tension coupling scenario. With very conservative arguments, we find that the radion mass is of the order of 10-2 GeV. The gravity is localized on the visible brane, and the spectrum of the gravitational KK modes is discrete and can be of the order of TeV. The corrections to the four-dimensional Newtonian potential from the higher order of gravitational KK modes are exponentially suppressed and can be safely neglected in current experiments. In an appendix, we also present a systematical and pedagogical study of the Gauss–Codacci equations and Israel's junction conditions across a (D - 1)-dimensional hypersurface, which can be either spacelike or timelike.

The Riemann–Lanczos equations in general relativity and their integrability

The aim of this paper is to examine the Riemann-Lanczos equations and how they can be made integrable. They consist of a system of linear first-order partial differential equations that arise in general relativity, whereby the Riemann curvature tensor is generated by an unknown third-order tensor potential field called the Lanczos tensor. Our approach is based on the theory of jet bundles, where all field variables and all their partial derivatives of all relevant orders are treated as independent variables alongside the local manifold coordinates (xa) on the given space-time manifold M. This approach is adopted in (a) Cartan’s method of exterior differential systems, (b) Vessiot’s dual method using vector field systems, and (c) the Janet–Riquier theory of systems of partial differential equations. All three methods allow for the most general situations under which integrability conditions can be found. They give equivalent results, namely, that involutivity is always achieved at all generic points of the jet manifold M after a finite number of prolongations. Two alternative methods that appear in the general relativity literature to find integrability conditions for the Riemann–Lanczos equations generate new partial differential equations for the Lanczos potential that introduce a source term, which is nonlinear in the components of the Riemann tensor. We show that such sources do not occur when either of method (a), (b), or (c) are used.

Adaptive Rational Interpolation: Arnoldi and Lanczos-like Equations

The Arnoldi and Lanczos algorithms, which belong to the class of Krylov subspace methods, are increasingly used for model reduction of large-scale systems. The standard versions of the algorithms tend to create reduced order models that poorly approximate low frequency dynamics. Rational Arnoldi and Lanczos algorithms produce reduced models that approximate dynamics at various frequencies. This paper tackles the issue of developing simple Arnoldi and Lanczos equations for the rational case. This allows a simple error analysis to be carried out for both algorithms and permits the development of computationally efficient model reduction algorithms, where the frequencies at which the dynamics are to be matched can be updated adaptively.

Stability analysis of dynamic thin shells

We analyse the stability of generic spherically symmetric thin shells to linearized perturbations around static solutions. We include the momentum flux term in the conservation identity, deduced from the ‘ADM’ constraint and the Lanczos equations. Following the Ishak–Lake analysis, we deduce a master equation which dictates the stable equilibrium configurations. Considering the transparency condition, we study the stability of thin shells around black holes, showing that our analysis is in agreement with previous results. Applying the analysis to traversable wormhole geometries, by considering specific choices for the form function, we deduce stability regions and find that the latter may be significantly increased by considering appropriate choices for the redshift function.

Letter: A Solution of the Weyl–Lanczos Equations for the Schwarzschild Space-Time

The spin coefficient form of the Weyl–Lanczos equations is analysed for the Schwarzschild space-time. The solution obtained yields an alternative form of Lanczos coefficients to the one currently known for this particular metric.

The Weyl–Lanczos relations and the four-dimensional Lanczos tensor wave equation and some symmetry generators

We examine symmetry generators for exterior differential systems and for systems of partial differential equations and apply the Cartan theory of exterior differential systems to the Weyl–Lanczos equations and to the Lanczos wave equation in four dimensions. We look at a number of examples of symmetries for the Weyl–Lanczos equations in four dimensions and give examples of isovectors when the solution manifold is the Schwarzschild, Kasner or Gödel space–time. Solutions of the Weyl–Lanczos system are automatically solutions of the Lanczos wave equation. We give examples of symmetry generators for the Lanczos wave equation and find that they are not automatically symmetry generators for the Weyl–Lanczos equations.

The Weyl–Lanczos equations and the Lanczos wave equation in four dimensions as systems in involution

The Weyl–Lanczos equations in four dimensions form a system in involution. We compute its Cartan characters explicitly and use Janet–Riquier theory to confirm the results in the case of all space–times with a diagonal metric tensor and for the plane wave limit of space–times. We write the Lanczos wave equation as an exterior differential system and, with assistance from Janet–Riquier theory, we compute its Cartan characters and find that it forms a system in involution. We compare these Cartan characters with those of the Weyl-Lanczos equations. All results hold for the real analytic case.