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In the present paper, we explore wormholes in [R.sup.2]-gravity within thef(R, T) formalism by using b(r) = [mathematical expression not reproducible] (hybrid shape function). The functional form f(R, T) = R + [alpha][R.sup.2] + [lambda]T is considered where R and T are the Ricci scalar and trace of the energy-momentum tensor, respectively, and a and A are controlling parameters. With the help of the EoS, [omega] = [p.sub.r]/[rho], geometric behavior is analyzed and energy conditions are discussed in the anisotropic scenario. In this investigation, significant contribution of the quadratic geometric term ([R.sup.2]) and linear trace term (T) are shown to validate energy conditions for the specific shape function and analyze wormhole solutions in the absence of exotic matter. Also, we observe that the energy conditions are valid in the whole range (r [greater than or equal to] [r.sub.0]) in the case of constant redshift function with this shape function. Key words: f(R, T) gravity, wormholes, energy conditions, shape function, modified gravity, cosmology. Nous explorons ici les trous de ver en gravite [R.sup.2] a l'interieur du formalisme f(R, T) en utilisant b(r) = [mathematical expression not reproducible] (fonction de forme hybride). Nous retenons la formule f(R, T) = R + [alpha][R.sup.2] + [lambda]T, avec R et T respectivement le scalaire de Ricci et la race du tenseur energie-impulsion, a et A etant des parametres de controle. Avec l'aide de l'equation d'etat (EdE/EoS) [omega] = [p.sub.r]/[rho], nous analysons le comportement geometrique et discutons les conditions sur l'energie dans un scenario anisotrope. Notre examen montre qu'une contribution significative du terme quadratique en R et du terme lineaire en T est necessaire afin de valider les conditions sur l'energie pour des fonctions de forme specifiques et afin d'observer des solutions trous de ver en l'absence de matiere exotique. Nous voyons aussi que les conditions sur l'energie sont valides dans tout le domaine r [greater than or equal to] [r.sub.0] dans le cas d'un decalage vers le rouge constant avec cette fonction de forme. [Traduit par la Redaction] Mots-cles : gravite f(R, T), trous de ver, fonction de forme, conditions sur l'energie, gravite modifiee, cosmologie., 1. Introduction Wormholes are a physical phenomenon that joins two different space-times or two different points on the same space-time. The concept of a wormhole was proposed by Flamm in [...]

In the present article, we study the physical and geometric scenario of the inflection of the Friedmann-LemaitreRobertson-Walker (FLRW) and an axially symmetric perfect fluid Universe with thick domain walls in f(R, T) theory of gravitation (Harko et al. Phys. Rev. D, 84,024020 (2011)), where R and T represent Ricci scalar and trace of the stress-energy-momentum tensor, respectively, in the scenario of decelerating-accelerating transition phases. To ascertain the exact solution of the corresponding field equations, we use the concept of a time-subordinate deceleration parameter, which brings forth the scale factor a(t) = [sinh.sup.1/n]([alpha]t), where n and [alpha] are positive parameters. For n [member of] (0.27,1], a class of accelerating phase is ensured while for n > 1, the Universe attains a phase transition from positive (decelerating) to negative (accelerating), which is uniform with recent observations. The models have been tested for physical feasibility by using stability. Physical and geometric behavior of the models are also explored. Key words: Friedmann-Robertson-Walker, f(R, T) gravity, domain walls, axially symmetric, transition universe. Nous etudions ici le cadre physique et geometrique du point d'inflexion d'un univers de fluide parfait de FriedmannLemaitre-Robertson-Walker (FLRW) a symetrie axiale (SA) parfaite avec murs de domaine epais dans une theorie f(R, T) de la gravite (Harko et al. Phys. Rev. D, 84, 024020 (2011)), ou R est le scalaire de Ricci et T est la trace du tenseur energie-impulsion, dans un scenario de transition de phases deceleration-acceleration. Pour nous assurer d'une solution exacte des equations de champ correspondantes, nous utilisons le concept d'un parametre de deceleration (PD/DP) qui met en scene le facteur d'echelle a(t) = [sinh.sup.1/n]([alpha]t), ou n et a sont des parametres positifs. L'intervalle n [member of] (0.27,1], garantit une classe de phase d'acceleration, alors que pour n > 1, l'univers atteint une transition de phase de positive (deceleration) a negative (acceleration), conforme aux observations recentes. Les modeles ont ete testes pour leur validite physique en utilisant la stabilite. Nous analysons les comportements plus ou moins physiques et geometriques des modeles. [Traduit par la Redaction] Mots-cles : Friedmann-Lemaitre-Robertson-Walker, gravite f(R, T), murs du domaine, symetrie axiale, univers en transition., 1. Introduction The present acceleration of the expansion of the Universe is one of the most challenging problems in modern cosmology. Different cosmic observations [1-15] indicate that expansion of the [...]

There is an unavoidable association of traversability of wormholes to the violation of null energy condition which in turn indicates the presence of exotic or non-exotic matter in the wormhole geometry. The exotic matter possesses the negative energy that is required to sustain the wormhole. Recently studies are done to solve this problem so as to avoid the exotic matter. In this work, we attempt to find such solution in the framework of F (R , T) gravity where F (R , T) = R + 2 λ T , here R and T are Ricci scalar and trace of energy momentum tensor respectively, using the Yukawa–Casimir shape function. For Yukawa–Casimir wormhole, it is assumed that the exotic energy is sourced from the Casimir energy density. We have examined the energy conditions using Yukawa–Casimir shape function b (r) = 2 r 0 3 + r 0 2 3 r exp − μ r − r 0 , where μ is a positive mass scale. We have taken different values of μ to study the role of Yukawa–Casimir energy in formation of traversable wormholes. The equilibrium aspect of the model is also investigated with the help of TOV equation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Casimir energy is always suggested as a possible source to create a traversable wormhole. It is also used to demonstrate the existence of negative energy, which can be created in a lab. To generalize this idea, Yukawa modification of a Casimir source has been considered in Remo Garattini (Eur. Phys. J. C 81 no.9, 824, 2021). In this work, we explore the Yukawa–Casimir wormholes in symmetric teleparallel gravity. We have taken four different forms of f (Q) to obtain wormhole solutions powered by the original Casimir energy source and Yukawa modification of the Casimir energy source. In power law form f (Q) = α Q 2 + β and quadratic form f (Q) = α Q 2 + β Q + γ , where α , β , γ are constants and Q is non-metricity scalar, we analyze that wormhole throat is filled with non-exotic matter. We find self-sustained traversable wormholes in the Casimir source where null energy conditions are violated in all specific forms of f (Q) , while after Yukawa modification, it is observed that violation of null energy conditions is restricted to some regions in the vicinity of the throat. [ABSTRACT FROM AUTHOR]

In this paper, we explore traversable wormhole solutions in different cases of modified F (R , T) theories of gravity. We have taken the functional form F (R , T) = R + α R 2 + λ T , where R is Ricci scalar and T is the trace of energy momentum tensor, while α and λ are constants. The different forms of R 2 -gravity in f (R , T) , f (R) frameworks and f (R , T) = R + λ T gravity are analyzed with its geometric behavior. The energy conditions are also discussed in the isotropic scenario using EoS ω = p r ρ and hybrid shape function b (r) = r 0 2 exp (r 0 − r) r , where r 0 is the throat radius. In this investigation, we found that quadratic geometric term and linear trace term of f (R , T) gravity and hybrid shape function play a significant contribution to validate the energy conditions for nonexotic wormhole solutions. [ABSTRACT FROM AUTHOR]

In this work, new Tsallis holographic dark energy (NTHDE) with future event horizon as IR-cutoff is constructed in a non-flat Friedmann–Lemaitre–Robertson–Walker Universe. The accelerating expansion phase of the universe is described by using deceleration parameter, equation of state parameter and density parameter by using different values of NTHDE parameter " δ " and " c ". We specifically derive the differential equations for the dark-energy density parameter (DP) and hence the equation of state parameter (EoS) by taking into account closed and open spatial geometry. In both a closed and an open universe, the equation of state parameter exhibits pure quintessence behavior for c > 1 , quintom behavior for c < 1 , and Λ CDM model recovery for c = 1. We can see the phase changes from deceleration to acceleration at z ≈ 0. 6 by tracking the evolution of the deceleration parameter. As inferred from the evolution of the Hubble parameter, NTHDE in a non-flat universe precisely matches Hubble data. Stability of our model by analyzing the squared speed of sound is investigated as well. [ABSTRACT FROM AUTHOR]

The presence of exotic matter for the existence of the wormhole geometry has been an unavoidable problem in GR. In recent studies, researchers have tried to deal with this issue using modified gravity theories where the WH geometry is explained by the extra curvature terms and NEC's are not violated signifying the standard matter in the WH geometry. In this paper, we investigate the solutions of traversable wormholes with normal matter in the throat within the framework of symmetric teleparallel gravity f (Q) , where Q is the non-metricity scalar that defines the gravitational interaction. We analyze the wormhole geometries for three forms of function f (Q). First is the linear form f (Q) = α Q , second a nonlinear form f (Q) = α Q 2 + β and third one a more general quadratic form f (Q) = α Q 2 + β Q + γ with α , β and γ being the constants. For all the three cases, the shape function is taken as b (r) = r 0 ln (r + 1) ln (r 0 + 1) where r 0 is the throat radius. A special variable redshift function is considered for the discussion. All the energy conditions are then examined for the existence and stability of the wormhole geometry. [ABSTRACT FROM AUTHOR]

In the present paper, we explore wormholes in R2-gravity within the f(R, T) formalism by using --> b (r) = r e r 0 − r --> (hybrid shape function). The functional form f(R, T) = R + αR2 + λT is considered where R and T are the Ricci scalar and trace of the energy–momentum tensor, respectively, and α and λ are controlling parameters. With the help of the EoS, ω = pr/ρ, geometric behavior is analyzed and energy conditions are discussed in the anisotropic scenario. In this investigation, significant contribution of the quadratic geometric term (R2) and linear trace term (T) are shown to validate energy conditions for the specific shape function and analyze wormhole solutions in the absence of exotic matter. Also, we observe that the energy conditions are valid in the whole range (r ≥ r0) in the case of constant redshift function with this shape function. [ABSTRACT FROM AUTHOR]

In this work, the solutions of traversable wormholes are investigated inside modified f (R) gravity under non-commutative geometry since matter possesses Lorentzian density distribution of a particle-like gravitation source. To find the exact wormhole solutions, two different shape functions b (r) = r 0 ( a r a r 0 ) , 0 < a < 1 , and b (r) = r 0 (cosh (r 0) cosh (r)) μ , 0 < μ < 1 , are considered. The first shape function was proposed by Mishra and Sharma [A new shape function for wormholes in f (R) gravity and General Relativity, preprint (2020), arXiv:2003.00298v1 [physics.gen-ph]], however the second is newly defined in this paper. The behaviors of both shape functions are analyzed with the throat radius r = r 0 = 1. The equation-of-state (EoS) parameter energy conditions, and anisotropy parameter are discussed with graphical point of view. [ABSTRACT FROM AUTHOR]

The concept of traversable wormhole, a hypothetical tunnel-like structure is initially proposed by Morris and Thorne (Am. J. Phys.56, 395 (1988)) by using Einstein's general relativity theory. Harko et al. (Phys. Rev. D84, 024020 (2011)) defined F (R , T) gravity as an extended gravitational theory having terms R and T as Ricci scalar and trace of energy momentum respectively. In this article, we explore wormhole models for the framework of F (R , T) gravity by using two different shape functions. The first shape function is b (r) = r 0 a r a r 0 , a ∈ (0 , 1) (proposed by Mishra and Sharma, arXiv:2003.00298v1 , 2020) and second is a hyperbolic shape function which is of the form b (r) = r 0 cosh (r 0) cosh (r) . Geometrical behavior of wormholes are discussed in anisotropic scenario by using equation of state ω = p r ρ . The stability of models are analyzed by using equilibrium condition and determining gravitational force, anisotropic force, hydrostatic force and force due to modified gravity. For the validation of null energy condition and weak energy condition, significant role of shape function is illustrated for the presence of nonexotic matter. [ABSTRACT FROM AUTHOR]

Differential subordination and superordination results associated with a generalized Hurwitz-Lerch Zeta function in the open unit disk are obtained by investigating appropriate classes of admissible functions. In particular some inequalities for generalized Hurwitz-Lerch Zeta function are obtained. [ABSTRACT FROM AUTHOR]