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Collapsing shear-free perfect fluid spheres with heat flow. (English) Zbl 1246.83154

Summary: A global view is given upon the study of collapsing shear-free perfect fluid spheres with heat flow. We apply a compact formalism, which simplifies the isotropy condition and the condition for conformal flatness. The formulas for the characteristics of the model are straight and tractable. This formalism also presents the simplest possible version of the main junction condition, demonstrated explicitly for conformally flat and geodesic solutions. It gives the right functions to disentangle this condition into well known differential equations like those of Abel, Riccati, Bernoulli and the linear one. It yields an alternative derivation of the general solution with functionally dependent metric components. We bring together the results for static and time-dependent models to describe six generating functions of the general solution to the isotropy equation. Their common features and relations between them are elucidated. A general formula for separable solutions is given, incorporating collapse to a black hole or to a naked singularity.

MSC:

83C75 Space-time singularities, cosmic censorship, etc.
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
80A10 Classical and relativistic thermodynamics
83C15 Exact solutions to problems in general relativity and gravitational theory
83C57 Black holes
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