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The paper traces the origin of the Middle East conflict and discusses the gradual evolution of the Israel-Palestine conflict from a historical perspective. The paper discusses the peace negotiations undertaken for the region during different periods and the contribution of the international community in reaching a compromise formula. The paper discusses the emergence and the role of Hamas and how it gained political legitimacy. The paper concludes with the views of Israel and India perspective. [ABSTRACT FROM AUTHOR]

This paper deals with the study of quasi-spherical gravitational collapse in the framework of f (R , T) theory. We will divide geometry of the star into two distinct portions i.e. interior portion and exterior portion. In the interior portion, we consider quasi-spherical Szekeres line element and in the exterior portion we take Vaidya line element. The interior and exterior portions will be glued by using Israel's junction conditions [W. Israel, Il Nuovo Cimento B (1965–1970) 44, 1 (1966); W. Israel, Phys. Lett. A 24, 184 (1967)]. The field equations will be derived in the context of f (R , T) theory for a particular model. Apparent horizons and their time configuration for various desirable cases will also be discussed. [ABSTRACT FROM AUTHOR]

In this paper, we inspect the stable geometry of thin-shell wormholes in the background of static spherically-symmetric AdS black holes solution bounded by dark fluid and Chaplygin-like equation of state p = − ℬ / ρ , where p and ρ denote the pressure and energy density that are related through positive constant ℬ. For this purpose, we consider the two equivalent copies of black holes and connected them at the hypersurface through cut and paste approach. Then, we employ the linearized radial perturbation to discuss the stability of the developed wormhole geometry by assuming variable equations of state. We obtain the maximum stable configuration for massive black holes for both barotropic and Chaplygin variable equations of state while for higher values of n , stable regions decrease. It is found that for every selection of physical parameters of black hole geometry with low intensity of Chaplygin dark fluid, we get the stable configuration of thin-shell wormholes. [ABSTRACT FROM AUTHOR]

This paper explores the role of nonlinear electrodynamics on the stable configuration of thin-shell wormholes formulated from two equivalent geometries of Reissner–Nordström black hole with nonlinear electrodynamics. For this purpose, we use cut and paste approach to eliminate the central singularity and event horizons of the black hole geometry. Then, we explore the stability of the developed model by considering different types of matter distribution located at thin-shell, i.e. barotropic model and variable equations of state (phantomlike variable and Chaplygin variable models). We use linearized radial perturbation to explore the stable characteristics of thin-shell wormholes. It is interesting to mention that Schwarzschild and Reissner–Nordström black holes show the unstable configuration for such type of matter distribution while Reissner–Nordström black hole with nonlinear electrodynamics expresses stable regions. It is found that the presence of nonlinear electrodynamics gives the possibility of a stable structure for barotropic as well as variable models. It is concluded that stable region increases for these models by considering higher negative values of coupling constant α and the real constant n. [ABSTRACT FROM AUTHOR]

This paper studies the complex mechanism of evolving charged self-gravitational (dissipating or non-dissipating) systems using a structure scalar Y T F , resulting from the basic procedure of orthogonal decomposition of the Riemann–Christoffel curvature tensor. The influence of electrical charge on the complexity of the considered system is analyzed in detail. We find several analytical Einstein–Maxwell models fulfilling the quasi-homologous ( Q H ) evolution plus the vanishing complexity factor ( C F ′ ) condition. Few of the presented models fulfill the Darmois constraints and exhibit shells, however, others satisfy the Israel constraints on both the boundary surfaces. Finally, some possible applications of the presented solutions are mentioned, which are important from astrophysical stand points. It is expected that some of the provided evolving Einstein–Maxwell fluid configurations may be utilized as a toy model of general frameworks like supernova explosions. It is found that the Q H implies the vanishing of the C F and gives rise to a unique and simplest configuration (Friedmann–Lemaître–Robertson–Walker model) fulfilling the condition Y T F = 0 and evolving in the Q H regime. [ABSTRACT FROM AUTHOR]

This paper examines the structure of gravastar (gravitationally vacuum star) in the background of f (ℜ , 2) theory. The gravastar can be regarded as a substitute for a black hole comprising of three regions (i) the interior domain, (ii) the intrinsic shell and (iii) the exterior domain. We investigate these domains by employing Karmarkar's condition by assuming a specific f (ℜ , 2) model. The field equations are solved to evaluate nonsingular solutions of both the interior and intermediate regions. Inner as well as outer spacetimes are matched together using Israel formalism to obtain density and pressure at the joining surface. Different attributes of gravastar like the equation of state parameter, proper length, entropy and energy are analyzed through graphical behavior. It is found that the gravastar model is a viable alternative to the black hole in the context of this gravity. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper examines the structure of a gravitational vacuum star (also known as gravastar) in the background of f (ℜ , 2) theory. This hypothetical object can be treated as a substitute of a black hole, with three regions: (i) the internal region, (ii) the intrinsic shell and (iii) the outer region. We examine these geometries using Finch–Skea metric for the radial metric component along with the particular f (ℜ , 2) model. We determine singularity-free solutions for both the inner as well as thin-shell domains. The smooth matching of the interior region with external Schwarzschild spacetime is obtained through Israel matching constraints. Finally, we study various characteristics of gravastar domains including the equation-of-state parameter, proper length, entropy, energy as well as surface redshift. It is found that the compact gravastar structure is a viable alternate to the black hole in the perspective of this gravity. [ABSTRACT FROM AUTHOR]

Let G be a finite group and ψ (G) = ∑ g ∈ G o (g) , where o (g) denotes the order of g. The function ψ ′ ′ (G) = ψ (G) / | G | 2 was introduced by Tărnăuceanu. In [M. Tărnăuceanu, Detecting structural properties of finite groups by the sum of element orders, Israel J. Math. (2020), doi:10.1007/s11856-020-2033-9], some lower bounds for ψ ″ (G) are determined such that if ψ ″ (G) is greater than each of them, then G is cyclic, abelian, nilpotent, supersolvable and solvable. Also, an open problem aroused about finite groups G such that ψ ″ (G) is equal to the amount of each lower bound. In this paper, we give an answer to the equality condition which is a partial answer to the open problem posed by Tărnăuceanu. Also, in [M. Baniasad Azad and B. Khosravi, A criterion for p-nilpotency and p-closedness by the sum of element orders, Commun. Algebra (2020), doi:10.1080/00927872.2020.1788571], it is shown that: If ψ ″ (G) > ψ ″ (D 2 p) , where p is a prime number, then G ≅ O p (G) × O p ′ (G) and O p (G) is cyclic. As the next result, we show that if G is not a p -nilpotent group and ψ ″ (G) = ψ ″ (D 2 p) , then G ≅ D 2 p . [ABSTRACT FROM AUTHOR]

In this paper, we analyze a few physical characteristics of gravastar with cylindrical geometry in f (R , T) theory, where R is the Ricci scalar and T is the trace of energy-momentum tensor. The gravastar is generally considered to be a substitute of a black hole with three different regions. In this work, we examine the formulation of gravastar-like cylindrical structures in f (R , T) theory. By using Darmois and Israel matching conditions, we formulate a mass function of a thin shell. We calculate the different physical characteristics of gravastar, in particular, entropy within the thin shell, proper length of the intermediate thin shell as well as energy of the shell. [ABSTRACT FROM AUTHOR]

The cosmological model executing hybrid expansion law (HEL) of scale factor in Randall–Sundrum type II (RS) braneworld gravity with Gauss–Bonnet terms in the presence of bulk viscosity described by Eckart theory, Truncated Israel–Stewart (TIS) theory, Full Israel–Stewart (FIS) theory and nonlinear Israel–Stewart (nIS) theory is studied. In the hybrid expansion law, the scale factor of the universe is described by the product of power-law and exponential expansions. In the HEL model, the early inflation and its transition from deceleration phase to present accelerated phase of expansion can be explored. The constraints of hybrid expansion law model parameters are determined using the recent observational data. Thereafter, the estimated parameters are considered to explore the present value of deceleration parameter, jerk parameter and transition epoch from early deceleration to the present accelerating phase. [ABSTRACT FROM AUTHOR]

Spherical energy shells in General Relativity tend to collapse due to gravitational effects and/or due to tension effects. Shell stabilization may be achieved by modifying the gravitational properties of the background spacetime. Thus, gravastars consist of stiff matter shells with an interior deSitter space and an exterior Schwarzshild spacetime whose attractive gravity balances the interior repulsive gravity of the interior deSitter spacetime leading to a stable stiff matter shell. Similar stabilization effects may be achieved by considering rotating shells. Here we study the stability of slowly rotating fluid shells. We show that the angular velocity of the shell has stabilizing properties analogous to the repulsive deSitter gravity of the interior of a gravastar. We thus use the Israel junction conditions [W. Israel, Nuovo Cim. B44S10 (1966) 1, Erratum: Nuovo Cim. B48 (1967) 463; N. Deruelle, M. Sasaki and Y. Sendouda, Prog. Theor. Phys.119 (2008) 237, arXiv:0711.1150 [gr-qc]] and the fluid equation of state of the rotating shell to construct the dynamical equations that determine the evolution of the rotating shell radius. These dynamical equations depend on the parameters of the background spacetime and on the angular velocity of the shell. Assuming a rotating interior and a Schwarzschild exterior spacetime we show that the angular velocity of the shell has interesting stabilizing properties on the evolution of its radius R. Thus, rotating matter (or vacuum) shells can imitate black holes while avoiding the presence of a singularity and without the presence of an interior deSitter space. [ABSTRACT FROM AUTHOR]

We consider a free massive quantized Klein–Gordon field in a spacetime (M , g) containing a stationary bifurcate Killing horizon, i.e. a bifurcate Killing horizon whose Killing vector field is globally time-like in the right wedge ℳ + associated to the horizon. We prove the existence of the Hartle–Hawking–Israel (HHI) vacuum state, which is a pure state on the whole spacetime whose restriction to ℳ + is a thermal state ω T H for the time-like Killing field at Hawking temperature T H = κ (2 π) − 1 , where κ is the surface gravity of the horizon. We show that the HHI state is a Hadamard state and is the unique Hadamard state which is equal to the double T H − 1 -KMS state in the double wedge ℳ − ∪ ℳ + . We construct the HHI state by Wick rotation in Killing time coordinates, using the notion of the Calderón projector for elliptic boundary value problems. [ABSTRACT FROM AUTHOR]