Junction Conditions Research Articles

Approximation of eigenvalues and eigenfunctions of the diffusion operator in a domain containing thin tubes by asymptotic domain decomposition method

We consider the spectral problem for the diffusion operator considered in a domain containing thin tubes. A new version of the method of partial asymptotic decomposition of the domain is introduced to reduce the dimension inside the tubes, getting a model of hybrid dimensions. The method truncates the tubes at some small distance from the ends of the tubes and replaces the longer part of the tubes with segments. At the interface of the three-dimensional and one-dimensional subdomains, special junction conditions are set: the pointwise continuity of the flux and the continuity of the average over a cross-section of the eigenfunctions. We obtain conditions on the ratio of the characteristic sizes in the transverse and longitudinal directions that ensure the closeness of two spectra, i.e. of the diffusion operator in the full-dimensional domain and the partially reduced one, keeping the conservation of the multiplicity, all up to a prescribed accuracy.

Anisotropic stellar structures in energy–momentum squared theory with Tolman–Kuchowicz spacetime

This paper examines the viable characteristics of anisotropic compact stars in [Formula: see text] theory ([Formula: see text] is the Ricci scalar and [Formula: see text]). In this perspective, we use Tolman–Kuchowicz solutions [Formula: see text] and [Formula: see text] to examine the configurations of static spherically symmetric structures. The unknown constants are found by the first fundamental form of Darmois junction conditions. We analyze the behavior of fluid parameters in the interior of 4U 1538-52, PSRJ 1614-220, EXO 1785-248 and SAXJ 1808.4-3658 compact stars correspond to different models of this theory. Furthermore, the stability of the proposed compact stellar objects is examined through sound speed and adiabatic index methods. The satisfaction of requisite conditions ensures that stable compact objects exist in this framework.

Einstein-Gauss-Bonnet dark matter halo: negative masses, rotation curves and the origin of dark matter effects

This work presents a novel approach to address the longstanding challenge posed by the rotation curves of galaxies and the associated missing mass problem. Utilizing the four-dimensional modified gravity framework of Einstein-Gauss-Bonnet (EGB), we develop a new model that integrates the concept of dark matter featuring negative mass due to the Gauss-Bonnet term. Our methodology involves using the action of EGB with boundary terms to derive the Israel junction condition, allowing the formulation of a model featuring a spherical dark halo. The mass expression of this dark halo exhibits a remarkable proportionality to the radius r at large distances, forming the basis for subsequent analyses. The model’s implications extend to the dynamics of the early Universe, where we introduce a dynamic scalar field classified as Chameleon. Posting this scalar field as the origin of dark matter effects, we establish a crucial link between the coupling constant α and the scalar field through Z2 symmetry breaking via the effective potential. This connection enables a subtle description of velocity, reminiscent of Modified Newtonian Dynamics (MOND), providing insights into the gravitational interplay and dark matter dynamics. A pivotal aspect of our study involves a particular comparison of the model’s predictions with observational data sourced from SPARC datasets. The alignment of our theoretical outcomes with empirical evidence underscores the model’s efficiency and its potential contribution to our understanding of galactic rotation dynamics.

Membrane models as a means of propulsion in general relativity: super-luminal warp-drive that satisfies the weak energy condition

Presented are toy-models for sub-luminal and super-luminal warp-drives in 3+1 dimensions. The models are constructed in a chimeric manner—as different bulk space-times separated by thin membranes. The membranes contain perfect-fluid-like stress-energy tensors. The Israel junction conditions relate this stress-energy to a jump in extrinsic curvature across the brane, which in turn manifests as apparent acceleration in the bulk space-times. The acceleration on either side of the brane may be set individually by choice of model parameters. The Weak Energy Condition (WEC) is shown to be satisfied everywhere in both models. Although the branes in these toy models are not compact, it is demonstrated that super-luminal warp-drive is possible that satisfies the WEC. Additionally, the nature of these models provides framework for speculation on a mechanism for transition from sub-luminal to super-luminal warp. It is shown that the difference in extrinsic curvature across a thin membrane can yield a positive contribution to the Landau–Raychaudhuri equation, thus providing a means to evade some super-luminal warp-drive no-go theorems. Neither quantum effects nor stability of the models is considered.

A class of germs arising from homogenization in traffic flow on junctions

We consider traffic flows described by conservation laws. We mainly study a 2:1 junction (with two incoming roads and one outgoing road). At the mesoscopic level, the priority law at the junction is given by traffic lights, which are periodic in time; the traffic can also be slowed down by periodic in time flux-limiters. Looking at long-time behavior and on large space scale, we intuitively expect an effective junction condition to emerge, thus deriving a macroscopic model from the mesoscopic one. At the limit of the rescaling, we show rigorous homogenization of the problem and identify the effective junction condition, which belongs to a general class of germs (in the terminology of [B. Andreianov, K. H. Karlsen and N. H. Risebro, A theory of [Formula: see text]-dissipative solvers for scalar conservation laws with discontinuous flux, Arch. Ration. Mech. Anal. 201 (2011) 27–86; U. S. Fjordholm, M. Musch and N. H. Risebro, Well-posedness and convergence of a finite volume method for conservation laws on networks, SIAM J. Numer. Anal. 60(2) (2022) 606–630; M. Musch, U. S. Fjordholm and N. H. Risebro, Well-posedness theory for nonlinear scalar conservation laws on networks, Netw. Heterog. Media 17 (2022) 101–128]). The proof of homogenization requires two steps: our first key result is the identification of this germ and of a characteristic subgerm which determines the whole germ. The second key result is the construction of a family of correctors whose values at infinity are related to each element of the characteristic subgerm. This construction is indeed explicit at the level of some mixed Hamilton–Jacobi equations for concave Hamiltonians (i.e. fluxes). The solutions are found in the spirit of representation formulas for optimal control problems.

Spin interaction of nonrelativistic neutrons with an ultrashort laser pulse

The nonrelativistic Pauli equation is used to study the interaction of slow neutrons with an ultrashort laser pulse. In the extreme limit, the pulse is acting on the magnetic moment of the neutron only at one instant of time. We obtain the scattering amplitude by deriving the junction conditions for the Pauli wave function across the pulse. Explicit expressions are given for a beam of polarized plane wave neutrons subjected to a pulse of spatially constant magnetic field strength. Finally we provide crude numerical estimates for pulses with the highest intensity available today.

Constraining study of charged gravastars solutions in symmetric teleparallel gravity

This study explores the effect of charge on a special astronomical object known as a gravastar, which is viewed as an alternative to a black hole. Based on the conjecture put out by Mazur and Mottola in general relativity, the study primarily focuses on the consequences of f(Q) gravity. The internal domain, the intermediate shell, and the external domain are the three separate sections that make up a gravastar. Using a particular f(Q) gravity model that includes conformal Killing vectors to analyze these areas, we discover that the inner domain shows a repulsive force on the spherical shell since it is assumed that pressure is equivalent to negative energy density. The intermediate shell is made up of ultrarelativistic plasma and pressure, which is proportional to energy density and balances the repulsive force from the interior domain. For the exterior region, we use two approaches first we calculate the vacuum exact solution, and second, consider the Reissner–Nordström metric. Then, we match these spacetimes through junction conditions and explore the stability constraints for both cases. Our results show that charged gravastar solutions with non-singular physical parameters including length, energy, entropy, and equation of state parameter are physically realistic.

Analytic approximations for the primordial power spectrum with Israel junction conditions

This work compares cosmological matching conditions used in approximating generic pre-inflationary phases of the Universe. We show that the joining conditions for primordial scalar perturbations assumed by Contaldi [] are inconsistent with the physically motivated Israel junction conditions; however, performing general relativistic matching with the aforementioned constraints results in unrealistic primordial power spectra. Eliminating the need for ambiguous matching, we look at an alternative semianalytic model for producing the primordial power spectrum allowing for finite duration cosmological phase transitions. Published by the American Physical Society 2024

Impact of energy-momentum squared gravity on the geometry of stellar objects

This paper investigates the impact of energy–momentum squared gravity on the geometry of anisotropic compact stellar objects. In this perspective, we use the Tolman IV solution to examine the configuration of static spherically symmetric structures. The values of unknown constants are found by the first fundamental form of Darmois junction conditions. We consider four different models of this theory to analyze the behavior of physical quantities such as effective fluid parameters, anisotropy, energy constraints and equation of state parameters in the interior of considered compact stars. Sound speed and adiabatic index methods are used to determine the stability of proposed compact stars. It is found that the proposed compact stars are viable and stable in energy–momentum squared gravity.

Extending Anisotropic Interiors admitting Vanishing Complexity in Charged f (R, T) Theory

AbstractThis paper extends the definition of the complexity factor for a charged self‐gravitating structure in the background of gravity. For this purpose, the modified Einstein‐Maxwell field equations and the mass function in terms of interior charge are calculated corresponding to a static sphere. The Reissner‐Nordström exterior spacetime and match it with the spherical interior at the hypersurface to determine the junction conditions are adopted then. The curvature tensor is also decomposed orthogonally, resulting in several scalar functions. Only encompasses all the required parameters and fulfills the proposed criteria to be the complexity factor for the considered setup is noticed. Moreover, some constraints to minimize the degrees of freedom in the field equations are chosen. To achieve this, complexity‐free constraint with four additional conditions depending on the matter sector that lead to different models is employed. The stability of the developed models is also analyzed in the presence and absence of charge through the standard model by varying the values of the model parameter . The presence of charge in compact models corresponding to , a polytropic and a linear equation of state make them stable for specific values of is concluded.

General Relativistic Lagrangian Continuum Theories Part I: Reduced Variational Principles and Junction Conditions for Hydrodynamics and Elasticity

General Relativistic Lagrangian Continuum Theories Part I: Reduced Variational Principles and Junction Conditions for Hydrodynamics and Elasticity

An Eternal gravitational collapse in f(R) theory of gravity and their astrophysical implications

The present investigation explores a novel facet of gravitational collapse, surpassing conventional notions of black holes and naked singularities. In this work, we explore a new aspects on the final fate of Gravitational Collapse of a stellar system within the framework of f(R) gravity and find the continued homogeneous gravitational collapse: an eternal collapsing phenomenon. The exact solutions of field equations have been obtained in an independent way by the parametrization of the expansion scalar (Θ) governed by the interior spherically symmetric FLRW metric. We impose the Darmois junction condition required for the smooth matching of the interior region to the Schwarzschild exterior metric across the boundary hypersurface of the star. The junction conditions demand that the pressure is non-vanishing at the boundary and is proportional to the non-linear terms of f(R) gravity, and the mass function m(t,r) is equal to Schwarzschild mass M. The eight massive stars, namely Westerhout49−2,BAT99−98,R136a1,R136a2,WR24,Pismis24−1, λ−Cephei, and β−CanisMajoris with their known astrophysical data (masses and radii) are used to estimate the numerical values of the model parameters which allows us to study the solutions numerically and graphically. Here we have discussed two f(R) gravity models describing the collapse phenomenon. The singularity analysis of models is discussed via the apparent horizon and we have shown that stars tend to collapse for an infinite co-moving time in order to attain the singularity (an eternal collapsing phenomenon). We have also shown that our models satisfy the energy conditions and stability requirements for stellar systems.

Junction conditions in gravity theories with extra scalar degrees of freedom

Junction conditions in gravity theories with extra scalar degrees of freedom

Study of charged gravastar model in [formula omitted] gravity

In recent days gravastar has been a very lucrative alternative to black holes, as it does not suffer from the singularity problem as well and it is based on sound physical grounds. Modified Symmetric teleparallel equivalent of gravity also has seen quite a few successes in recent years both in cosmology as well as in astrophysical objects like black holes and wormholes. In this paper, we have considered the charged gravastar in f(Q) formulation and have solved it fully analytically and found various physical characteristics like energy density, entropy and EoS for the gravastar. We have used the Israel junction condition to make some phenomenological predictions regarding the potential of the thin shell around the gravastar. We have also studied the deflection of the angle caused by the gravastar. Finally, we conclude by noting how future radio telescopes could detect the gravastar shadow and how can one distinguish it from the black hole event horizon.

Stable gravastar with large surface redshift in Einstein's gravity with two scalar fields

We propose a class of models, in which stable gravastar with large surface redshift becomes a solution. In recent decades, gravastars have become a plausible substitute for black holes. Researchers have explored stable gravastar models in various alternative gravity theories, in addition to the conventional framework of general relativity. In this paper, we present a stellar model within the framework of Einstein's gravity with two scalar fields, in accordance with the conjecture proposed by Mazur and Mottola [Proc. Nat. Acad. Sci. 101 (2004), 9545-9550]. In the model, the two scalar fields do not propagate by imposing constraints in order to avoid ghosts. The gravastar comprises two distinct regions, namely: (a) the interior region and (b) the exterior region. We assume the interior region consists of the de Sitter spacetime, and the exterior region is the Schwarzschild one. The two regions are connected with each other by the shell region. On the shell, we assume that the metric is given by a polynomial function of the radial coordinate r. The function has six constants. These constants are fixed by the smooth junction conditions, i.e., the interior region with the interior layer of the shell and the exterior region with the exterior layer of the shell. From these boundary conditions, we are able to write the coefficients of the scalar fields in terms of the interior radius and exterior radius. To clarify the philosophy of this study, we also give two examples of spacetimes that asymptote as the de Sitter spacetime for small r and as the Schwarzschild spacetime for large r. Exploration is focused on the physical attribute of the shell region, specifically, its proper length. The gravastar model's stability has frequently been examined by analyzing the relationship between surface redshift and shell thickness, a comparison we also undertake with previous models. Especially, we show that there exists a stable gravastar with a large surface redshift prohibited by the instability in the previous works. Furthermore, by checking the effective equation of state parameters, we show that the gravastar geometry realized in this paper by using two scalar fields could be difficult to generate with ordinary fluid.

Dynamically Charged Spheres and their Stability in Einstein‐Gauss‐Bonnet Gravity

AbstractElectrically charged anisotropic fluid spheres with vanishing expansion scalar condition under the influence of a newly established gravitational scheme are investigated in this study, i.e., Einstein‐Gauss‐Bonnet (EGB) gravity. Glavan and Lin introduced this framework, in which they rescaled the coupling factor using and derived the gravitational field equations. The work of Herrera et al. is extended to explore the dynamical instability of charged spherically symmetric matter distribution in the context of EGB gravity. In this respect, dynamical equations, conservation equations, and junction conditions for charged sphere are computed. To study the evolution of considered system in the Newtonian and post‐Newtonian regimes against an expansion‐free background, several substantial restrictions are imposed employing a perturbation approach. This study showed that the adiabatic index () has no effect on the instability ranges in the aforementioned approximations. It is analyzed that the determination of these ranges solely attributed to the anisotropy of fluid surface pressures, radial profile, EGB factors, and charged intensity parameters along with the radial distribution of energy density.

Chronology Protection in f(T) Gravity: The Case of Gott’s Pair of Moving Cosmic Strings

As a consequence of the spacetime structure, defined by the tetrad field instead of the metric tensor alone, f(T) gravity seems to harbor its own chronology protection agency. When Gott’s pair of moving cosmic strings is considered, it is shown that the requirement of having a global parallelization—i.e., a global smooth field of tetrads– drastically restricts the form of the tetrads on the junction surface between the two strings. The junction conditions on the tetrad field are satisfied only if the corresponding boosts needed to put the strings in motion are null on the matching surface. This seems to throw overboard Gott’s construction from the outset without the need for analyzing the divergence of the expectation value of the energy–momentum tensor on the Cauchy horizon, evading in this way bothersome quarrels concerning the choice of vacuum.

Features of anisotropic compact stars in rastall teleparallel gravity via linear equation of state

This paper aims to discuss the model of compact stars based on spherically symmetric spacetime, with a focus on the gravitational effects of Rastall teleparallel gravity, where T represents torsion and λ represents the Rastall parameter. In this study, we evaluate the spherically symmetric spacetime component e a(r) in terms of e b(r) using the linear equation of state p r = β ρ + γ, while the other component e b(r) is assumed from the literature. The paper delves into a detailed analysis of various properties of compact stars such as energy density profile, pressure components, gradients profiles, anisotropic conduct, energy limits, equation of state profiles, velocities of sound profiles, TOV equation profiles, and compactification profile. We use the well-known junction conditions to facilitate the evaluation of the unknown parameters, taking the standard Schwarzschild metric as the outer spacetime. Through detailed analysis in graphical form, we demonstrate that the model showing the anisotropic conduct of stellar objects is viably legitimate, regular, and stable. Overall, the paper provides a comprehensive analysis of the properties of compact stars, which will undoubtedly contribute to our understanding of these astrophysical phenomena.

Dynamics of Cylindrical Collapse in Palatini Gravity

This research explores how filamentary objects behave when they collapse in the presence of exotic material. To accomplish this, we employ Palatini (R, T) theory as a candidate for exotic material. We derive the collapsing equation by enforcing the Darmois junction condition on the collapsed surface boundary. At this boundary, we obtain that the radial pressure is proportionate to the time‐dependent term of the field and is not zero. Lastly, we investigate the correlation between dark matter and gravitational waves and find that exotic terms disrupt the transmission of gravitational waves. It is worthwhile to mention here that our results (in both formalisms, metric approach and Palatini approach) reduce to (R) gravity and general relativity.

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.