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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:
83C75Space-time singularities, cosmic censorship, etc.
83C55Macroscopic interaction of the gravitational field with matter (general relativity)
80A10Classical thermodynamics, including relativistic
83C15Closed form solutions of equations in general relativity
83C57Black holes
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References:
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