Evolving spheres of shear-free anisotropic fluid

Abstract

The fluid models mentioned in the title are studied in a modified approach, based on two formulas for the mass function. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second order differential equation. Different constraints are imposed on this core of relations, finding new solutions and deriving the classical results for perfect fluids as particular cases. All charged anisotropic solutions, all conformally flat and all uniform density solutions are found. A large class of solutions with linear equation among the two pressures is derived, including the case of vanishing tangential pressure. The mechanism responsible for the appearance of equation of state is elucidated.

22 pages

References in corpus (11)

• All static spherically symmetric anisotropic solutions of Einstein's equations
• Structure and evolution of self-gravitating objects and the orthogonal splitting of the Riemann tensor
• On the role of density inhomogeneity and local anisotropy in the fate of spherical collapse
• Conformally flat anisotropic spheres in general relativity
• Shearing Expansion-free Spherical Anisotropic Fluid Evolution
• The importance of anisotropy for relativistic fluids with spherical symmetry
• Shear-free radiating collapse and conformal flatness
• Radiating Collapse with Vanishing Weyl stresses
• Expanding Spherically Symmetric Models without Shear
• Cosmic censorship and spherical gravitational collapse with tangential pressure
• Singularities in gravitational collapse with radial pressure

Cited by in corpus (7)

• Stable and self-consistent compact star models in teleparallel gravity
• Collapsing shear-free perfect fluid spheres with heat flow
• Modelling anisotropic fluid spheres in general relativity
• Anisotropic Compact Star Model Satisfying Karmarkar Conditions
• Collapse of a relativistic self-gravitating star with radial heat flux: Impact of anisotropic stresses
• Compact stellar model in higher torsion gravitational theory
• A New Class of Analytical Solutions Describing Anisotropic Neutron Stars in General Relativity