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We present a study of dissipative gravitational collapse in spherically symmetric gravitating spacetime by applying the Misner-Sharp approach in metric f(R, T) gravity. This work is an extension of the study by Herrera, Di Prisco, Fuenmayor, and Troconis, Int. J. Mod. Phys. D, 18,129 (2009), that was already done with the general theory of relativity. To this end, we have formulated a set of equations of motion by using f(R, T) = R + [lambda]T (where R is the Ricci scalar, T is the trace of stress-energy tensor, and [lambda] is the coupling constant), as well as a stress-energy tensor of viscous and heat conducting fluid. The conservation equations have been also derived for such setup. Both the conservation equations and equation of motion provide the dynamical equations in terms of the theory of gravity. Furthermore, the causal thermodynamic approach introduced by Muller-Israel-Stewart has been used to formulate the transportation equations of heat flux and bulk viscosity. Then, we perform the coupling of dynamical equations and transportation equations. The effects of bulk and shear viscosities have been investigated in detail. Finally, we studied the impact of the matter curvature coupling parameter A on the dynamics of the gravitating source. Key words: gravitational collapse, f(R, T) theory, viscous fluids, casual thermodynamics, heat transportation. Nous presentons ici une etude de l'effondrement gravitationnel dissipatif dans un espace-temps gravitant a symetrie spherique, par application de l'approche de Misner-Sharp en gravitef(R, T). Ce travail est une extension du travail de Herrera, Di Prisco, Fuenmayor, and Troconis, Int. J. Mod. Phys. D, 18,129 (2009), deja fait dans le cadre de la relativite generale. A cette fin, nous formulons un ensemble d'equation du mouvement en utilisantf(R, T) = R + [lambda]T, (ou R est le scalaire de Ricci, T est la trace du tenseur d'energie-impulsion et [lambda] une constante de couplage), avec le tenseur d'energie-impulsion et un fluide conducteur de chaleur. Les equations de conservation sont developpees dans ce cadre theorique. Ensemble, les equations de conservation avec les equations du mouvement fournissent les equations dynamiques requises dans cette theorie de la gravite. Nous utilisons egalement l'approche thermodynamique causale de Muller-Israel-Stewart, afin de decrire les equations de transport de chaleur et la viscosite de volume. Nous couplons les equations dynamiques et les equations de transport et etudions en detail les effets de la viscosite de volume et de cisaillement. Finalement, nous analysons l'impact du parametre de couplage A sur la dynamique de la source gravitante. [Traduit par la Redaction] Mots-cles: effondrement gravitationnel, theorief(R, T), fluides visqueux, thermodynamique causale, transport de chaleur., 1. Introduction The empirical data from the anisotropy of the supernova type Ia (SNela), large-scale structure, measurement of cosmic microwave background, and baryon acoustic oscillations [1-4] indicate that the current [...]

In this paper, we derive the exact solution of traversable wormholes illustrating spherically symmetric geometry with anisotropic matter distribution entering the throat in the formalism of f (ℛ ,) gravity, where ℛ is Ricci scalar and is trace of energy–momentum tensor. For this purpose, we assume a power law-type generic function f (ℛ ,) = ℛ + γ ℛ 2 + α , where γ and α are being constants, with two different choices of shape functions a (r) = r 0 ( b r b r 0 ) , 0 < a (r) < 1 and a (r) = r 0 (cosh (r 0) cosh (r)) μ , 0 < μ < 1. For each approach, we find the exact solution and studied the existence of wormhole solutions in the presence of exotic and non-exotic matter. The graphical behavior of equation of state (EoS) parameter and energy condition bounds is also investigated for each shape function. The realistic wormhole solutions are obtained for the shape functions which satisfy necessary conditions at the throat radius r = r 0 = 1. Finally, we observe that there is small deviation in the results obtained by General Relativity and f (ℛ 2 ,) gravity. [ABSTRACT FROM AUTHOR]

This study explores the impact of f (G,T) gravity, where G is the Gauss Bonnet invariant and T is the trace of the energy–momentum tensor, on the adiabatic anisotropic spherical gravitating source under the expansion-free condition. We coupled the relativistic matter with spherical symmetric structure by applying f (G,T) = α G n + λ T Gauss–Bonnet model with a linear trace. To derive the collapse equation, we used the perturbation method on the field equations and the contracted Bianchi identities. The dynamics of instability range is depicted in Newtonian (N) and post-Newtonian (pN) regimes. Furthermore, instead of using the adiabatic index, we establish the instability range by looking at the density profile and anisotropic pressure configuration. We investigate the analytic solutions that meets the expansion-free condition. Finally, we have successfully achieved the original results obtained by Herrera et al. (2012) in General Relativity by setting α = λ = 0 in proposed cosmological model. • Investigate how expansion-free condition affects adiabatic collapse in f (G,T) gravity. • Establish the instability range without using adiabatic index. • Discuss the role of a cosmological model with linear trace term. • Find analytic solutions that meet the expansion-free condition. • Use perturbation on field equations and Bianchi identities to derive collapse equation. [ABSTRACT FROM AUTHOR]

In this paper, we have used the Karmarkar condition to the spherically symmetric non-static radiating star experiencing dissipative gravitational collapse with a heat flux in the framework of f (R , T) gravity, (where R is Ricci scalar which replaces Lagrangian density and T is the trace of energy–momentum tensor). To obtain the ultimate results of the gravitational field equations in f (R , T) scenario, we take a linear form of the function as f (R , T) = R + 2 λ T. In this connection, the Karmarkar condition along with boundary condition generates a model of radiating star and enables us to completely indicate the spatial presence of gravitational potentials. Vadiya's exterior solution across a time-like hypersurface is smoothly matched to the interior solution which allows to study the physical conduct of our model under consideration. Furthermore, we have analyzed the energy conditions of radiating star in f (R , T) gravity and analyzed the physical behavior of thermodynamics parameters which provide a detailed discussion of the model. For coupling parameter λ = 0 , we successfully obtain the standard results of General Relativity. [ABSTRACT FROM AUTHOR]

We investigate the concept of complexity factor for a class of compact star in the framework of modified f (R , T) gravity. We obtain a generic form of hydrostatic equilibrium equation, express the Einstein field equations, mass function and also physical observation for linear form of function f (R , T) = R + 2 λ T , where λ is the coupling parameter, R is Ricci scalar and T is trace of energy momentum tensor. We have analyzed the properties of compact astrophysical objects like energy density and anisotropic pressure are affected by changing the values of coupling parameter λ . We obtained numerical outputs of some physical variables for different chosen values of coupling parameter λ to observe the effect of λ on these quantities and show these in tabular form for different compact stars 4 U 1820 - 30 , Her X - 1 , SAX J 1808.4 - 3658 and VelaX - 12 with radii 10, 7.7, 7.07 and 9.99 respectively. We determine structure scalars with orthogonal splitting of the Riemann tensor and with the help of these scalars the complexity factor can be determined. Furthermore, we have checked some astrophysical sources for vanishing complexity factor. [ABSTRACT FROM AUTHOR]

We explore the problem of charged perfect fluid spherically symmetric gravitational collapse in f(R, T) gravity (R is Ricci scalar and T is the trace of energy–momentum tensor). We have taken the interior boundary of a star as spherically symmetric metric filled with the charged perfect fluid. In order to study charged perfect fluid collapse, we have investigated the exact solutions of the Maxwell–Einstein field equations solutions using the most simplified form for f(R, T) model f(R, T) = R + 2 λ T, where λ is model parameter. This study involves the effects of charge as well as coupling parameter on collapse of a star. We studied the nature of trapped surfaces, apparent horizon and singularity structure in detail. It has been found that singularity is formed earlier than the apparent horizons, so the end state of gravitational collapse in this case is black hole. [ABSTRACT FROM AUTHOR]