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In this work, we employ the Karmarkar condition together with the notion of vanishing complexity (Herrera in Phys Rev D 97:044010, 2018) and isotropization technique to generate models of compact stars within the framework of complete geometric deformation. Starting off with the Kuchowicz ansatz as one of the metric potentials for the seed solution, we impose the Karmarkar condition to obtain fully the gravitational behaviour of a static compact object with anisotropic pressure. This solution is then subjected to the complete geometric deformation algorithm. The novelty in our work is to impose the condition of vanishing complexity and isotropization techniques in order to derive the deformation functions. We present two solutions of the resulting governing equations which are subjected to physical viability tests. We demonstrate that the presence of pressure anisotropy within the bounded object plays a key role in determining its stability. In addition, we show that the magnitude of the decoupling constant determines the direction of energy flow between the generic fluid and the fluid matter distribution. [ABSTRACT FROM AUTHOR]

In this work, we present a hierarchical solution-generating technique employing the Minimum Gravitational Decoupling (MGD) Method and the generalized concept of Complexity as applied to Class I spacetime for bounded compact objects in classical general relativity. Starting off with an anisotropic seed solution described by Class I spacetime, we apply the MGD technique with the constraint that the effective anisotropy vanishes which leads to an isotropic model. In addition, we produce a second family of solutions in which the Complexity factor [Herrera (Phys Rev D 97:044010, 2018)] for the seed solution and its MGD counterpart are the same. We discuss the physical plausibility of both classes of solutions as candidates for physically realizable compact objects. [ABSTRACT FROM AUTHOR]

In this work we explore the characteristics of a polytropic solution for the anisotropic stellar object within the framework of Einstein–Gauss–Bonnet (EGB) gravity. We introduce anisotropy via the minimally gravitational decoupling method. The analysis of the exact solution of the governing equation for the gravitational potentials reveals novel features of the compact object. We find that the EGB coupling constant and the decoupling parameter play important roles in enhancing and suppressing the effective density and radial profiles at each interior point of the bounded object. An analysis of the effective tangential pressure reveals a 'changeover' in the trends brought about by the EGB and decoupling constants which may be linked to the cracking observed in classical 4D stellar objects proposed by Herrera (Phys Lett A 165:206, 1992). [ABSTRACT FROM AUTHOR]

We model a radiating star undergoing dissipative gravitational collapse in the form of radial heat flux. The exterior of the collapsing star is described by the generalised Vaidya solution representing a mixture of null radiation and strings. Our model generalises previously known results of constant string density atmosphere to include inhomogeneities in the exterior spacetime. By utilising a causal heat transport equation of the Maxwell-Cattaneo form we show that relaxational effects are enhanced in the presence of inhomogeneities due to the string density. [ABSTRACT FROM AUTHOR]

Utilizing an ansatz developed by Maurya et al. we present a class of exact solutions of the Einstein-Maxwell field equations describing a spherically symmetric compact object. A detailed physical analysis of these solutions in terms of stability, compactness and regularity indicates that these solutions may be used to model strange star candidates. In particular, we model the strange star candidate Her X-1 and show that our solution conforms to observational data to an excellent degree of accuracy. An interesting and novel phenomenon which arises in this model is the fact that the relative difference between the electromagnetic force and the force due to the pressure anisotropy changing sign within the stellar interior. This may be an additional mechanism required for stability against cracking of the stellar object. [ABSTRACT FROM AUTHOR]

In this work we present an exact solution of the Einstein-Maxwell field equations describing compact charged objects within the framework of classical general relativity. Our model is constructed by embedding a four-dimensional spherically symmetric static metric into a five-dimensional flat metric. The source term for the matter field is composed of a perfect fluid distribution with charge. We show that our model obeys all the physical requirements and stability conditions necessary for a realistic stellar model. Our theoretical model approximates observations of neutron stars and pulsars to a very good degree of accuracy. [ABSTRACT FROM AUTHOR]

We present charged anisotropic Durgapal IV interior solutions of the general relativistic field equations in curvature coordinates. These exact solutions can be used to model stable and well-behaved compact stars. Using these solutions we have presented models of well-known neutron and quark stars such as PSR J1903+0327, RX-J1856.5-3754, PSR B1913+16, PSR J0737-3039A and Cyg X-2. The equation of state (EoS) corresponding to the modeled objects are studied using their compression moduli. According to our solutions it is found that the EoS for Cyg X-2 (neutron star) is stiffer than any other object presented and therefore more massive. Furthermore, the EoS for RX J1856.5-3754 (Quark star) is the softest one, rendering it least massive. These solutions satisfy all the energy conditions. Finally, all our presented stellar models satisfy the equilibrium condition of Cooperstock and de la Cruz i.e. M > Q . [ABSTRACT FROM AUTHOR]

The Kramer radiating star uses the interior Schwarzschild solution as a seed solution to generate a model of dissipative collapse. We investigate the thermal behaviour of the radiating star by employing a causal heat transport equation. The causal temperature is explicitly determined for the first time by integrating the transport equation. We further show that the dissipation of energy to the exterior space-time renders the core more unstable than the cooler surface layers. [ABSTRACT FROM AUTHOR]

We analyse a new family of solutions to the Einstein field equations describing the collapse of a fluid sphere in the presence of heat flux and shear. These solutions ensure that the collapsing fluid is accelerating and provide a generalisation of the geodesic fluid models studied in earlier treatments. In particular, we demonstrate the role played by pressure in the dynamics of the collapse process. [ABSTRACT FROM AUTHOR]

We investigate the role played by the cosmological constant during gravitational collapse of a radiating star with vanishing Weyl stresses in the interior. We highlight the role played by the cosmological constant during the latter stages of collapse. The evolution of the temperature of the collapsing body is studied by employing causal heat transport equation. We show that the inclusion of the cosmological constant enhances the temperature within the stellar core. [ABSTRACT FROM AUTHOR]

We model the gravitational behaviour of a radiating star when the exterior geometry is the generalised Vaidya spacetime. The interior matter distribution is shear-free and undergoing radial heat flow. The exterior energy momentum tensor is a superposition of a null fluid and a string fluid. An analysis of the junction conditions at the stellar surface shows that the pressure at the boundary depends on the interior heat flux and the exterior string density. The results for a relativistic radiating star undergoing nonadiabatic collapse are obtained as a special case. For a particular model we demonstrate that the radiating fluid sphere collapses without the appearance of the horizon at the boundary. [ABSTRACT FROM AUTHOR]

In this paper we revisit the problem of modeling radiating stars in which the areal radius is equal to the proper radius throughout the stellar evolution. We provide a new family of solutions that completely describes the dynamical behaviour of these so-called Euclidean stars. The solution satisfies all the energy conditions, and importantly, admits a barotropic equation of state. [ABSTRACT FROM AUTHOR]

We investigate the gravitational collapse of a radiating sphere evolving into a final static configuration described by the interior Schwarzschild solution. The temperature profiles of this particular model are obtained within the framework of causal thermodynamics. The overall temperature evolution is enhanced by contributions from the temperature gradient induced by perturbations as well as relaxational effects within the stellar core. [ABSTRACT FROM AUTHOR]

We present the general junction conditions for the smooth matching of a spherically symmetric, shear-free spacetime to Vaidya’s outgoing metric across a four-dimensional time-like hypersurface in the presence of a cosmological constant. These results generalise earlier treatments by Santos and co-workers on radiating stellar models. We study the thermal evolution of a particular radiating model within the framework of extended irreversible thermodynamics. [ABSTRACT FROM AUTHOR]

We investigate the causal temperature profiles in a recent model of a radiating star undergoing dissipative gravitational collapse without the formation of a horizon. It is shown that this simple exact model provides physically reasonable behaviour for the temperature profile within the framework of extended irreversible thermodynamics. [ABSTRACT FROM AUTHOR]

We present a simple nonstatic generalization of the isothermal universe. The cosmological fluid obeys a barotropic equation of state of the formp=a?. We employ a causal heat transport equation of the Maxwell-Cattaneo form to study the thermodynamical behavior of our model. [ABSTRACT FROM AUTHOR]

In this paper we present a simple generalisation of all spherically symmetric static solutions. We present a framework to obtain both anisotropic and isotropic models with and without a barotropic equation of state of the form p = αρ. The nonstaticity in some models necessarily requires a nonzero heat flux which dictates the thermodynamics of our models. [ABSTRACT FROM AUTHOR]

We investigate the effect of heat dissipation in inhomogeneous cosmologies by invoking the full causal theory of heat transport within the framework of extended irreversible thermodynamics. This work extends earlier results which were obtained using the truncated causal heat transport equation. In particular, we show that the truncation of the heat transport equation implicitly defines a temperature law which leads to pathological behaviour in the temperature of the evolving cosmic fluid. [ABSTRACT FROM AUTHOR]

We find a simple inflationary solution in aninhomogeneous spacetime with heat flux. The heat fluxobeys a causal transport equation, and counteracts theinflationary decrease of energy density. At late times, the heat flux tends to zero and thefluid approaches the equation of state p =–ρ. [ABSTRACT FROM AUTHOR]