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The goal of this work is to build a new family of stellar interior solutions in the anisotropic regime of pressure using the framework of gravitational decoupling via minimal geometric deformation. For such purpose, we use a generalization of the complexity factor of the well-known Wyman IIa ( n = 1) interior solution in order to close the Einstein’s Field Equations, as well we use the Wyman IIa, Tolman IV, and Heintzmann IIa and Durgapal IV models as seeds solutions. These models fulfill the fundamental physical acceptability conditions for the compactness factor of the system 4U 1820-30. Stability against convection and against collapse are also studied.

For mathematical simplicity reasons, vacuum solutions of the GR equations have been studied more often than their corresponding interiors. Among them, the Weyl-Lewis vacuum, gravitationally sourced by a stationary rotating cylinder of matter, has long been known and studied, while its interior spacetimes were left aside. Now, in a recent series of seven papers, a set of interior solutions matching a Weyl-Lewis exterior has been displayed. These new exact solutions to the field equations correspond to different configurations of fluid equations of state and rotation type, rigid and non-rigid. Here, both perfect fluid cases, rigidly and differentially rotating, are described and their physical properties are analyzed.

We search for exact analytical solutions of spherically symmetric dissipative fluid distributions satisfying the vanishing expansion condition (vanishing expansion scalar Θ). To accomplish this, we shall impose additional restrictions allowing integration of the field equations. The solutions are analyzed, and possible applications to astrophysical scenarios as well as alternative approaches to obtaining new solutions are discussed.

We establish a hierarchy of Euclidean stars according to their degree of complexity, as measured by the complexity factor and the complexity of the pattern of evolution. We consider both, non-dissipative and dissipative systems. Solutions range from the simplest one, in order of increasing complexity. Some specific models are found and analyzed in detail.

We explore an idea put forward many years ago by Zeldovich and Novikov concerning the existence of compact objects endowed with arbitrarily small mass. The energy density of such objects, which we call “ghost stars”, is negative in some regions of the fluid distribution, producing a vanishing total mass. Thus, the interior is matched on the boundary surface to Minkowski space–time. Some exact analytical solutions are exhibited and their properties are analyzed. Observational data that could confirm or dismiss the existence of this kind of stellar object are discussed.

We present a model of an evolving spherically symmetric dissipative self-gravitating fluid distribution which tends asymptotically to a ghost star, meaning that the end state of such a system corresponds to a static fluid distribution with a vanishing total mass and an energy density distribution which is negative in some regions of the fluid. The model was inspired by a solution representing a fluid evolving quasi-homologously and with a vanishing complexity factor. However, in order to satisfy the asymptotic behavior mentioned above, the starting solution had to be modified, as a consequence of which the resulting model only satisfies the two previously mentioned conditions asymptotically. Additionally, a condition on the variation in the infinitesimal proper radial distance between two neighboring points per unit of proper time was imposed, which implies the presence of a cavity surrounding the center. Putting together all these conditions, we were able to obtain an analytical model depicting the emergence of a ghost star. Some potential observational consequences of this phenomenon are briefly discussed in the last section.

This study focuses on the impact of the cosmological constant on hyperbolically symmetric matter configurations in a static background. I extend the work of Herrera et al. 2021. and describe the influences of such a repulsive character on a few realistic features of hyperbolical anisotropic fluids. After describing the Einstein-Λ equations of motion, I elaborate the corresponding mass function along with its conservation laws. In our study, besides observing negative energy density, I notice the formation of a Minkowskian core as matter content is compelled not to follow inward motion near the axis of symmetry. Three families of solutions are found in the Λ-dominated epoch. The first is calculated by keeping the Weyl scalar to a zero value, while the second solution maintains zero complexity in the subsequent changes of the hyperbolical compact object. However, the last model encompasses stiff fluid within the self-gravitating system. Such a type of theoretical setup suggests its direct link to study a few particular quantum scenarios where negative behavior of energy density is noticed at the Λ-dominated regime.

Exact solutions are presented which describe, either the evolution of fluid distributions corresponding to a ghost star (vanishing total mass), or describing the evolution of fluid distributions which attain the ghost star status at some point of their lives. The first two solutions correspond to the former case, they admit a conformal Killing vector (CKV) and describe the adiabatic evolution of a ghost star. Other two solutions corresponding to the latter case are found, which describe evolving fluid spheres absorbing energy from the outside, leading to a vanishing total mass at some point of their evolution. In this case the fluid is assumed to be expansion–free. In all four solutions the condition of vanishing complexity factor was imposed. The physical implications of the results, are discussed.

We study the general properties of dissipative fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. It is shown that the energy density is necessarily negative, and the central region cannot be attained by any fluid element. We describe this inner region by a vacuum cavity around the center. By assuming a causal transport equation some interesting thermodynamical properties of these fluids are found. Several exact analytical solutions, which evolve in the quasi–homologous regime and satisfy the vanishing complexity factor condition, are exhibited.

We present a class of exact solutions of Einstein's gravitational-field equations describing spherically symmetric and static anisotropic stellar-type configurations. The solutions are obtained by assuming a particular form of the anisotropy factor. The energy density and both radial and tangential pressures are finite and positive inside the anisotropic star. Numerical results show that the basic physical parameters (mass and radius) of the model can describe realistic astrophysical objects such as neutron stars.