A Simple Model for Gravitational Collapse with Pressure Gradient

概要

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A simple model for gravitational collapse with pressure gradient, but without energy flow, is investigated within the framework of general relativity. The model is regular at all times throughout the entire region in such a way that all interior events can send signals to external observers. The mass-radius relation of the model provides us with the inequality GM/c^2R_b<0.375, which is comparable with the analogous ones due to Buchdahl and Bondi for static fluid spheres. The usual assumption of quasi-static equilibrium is, however, prohibited in our model, because its fluid velocity can attain about one-tenth the speed of light. The gravitational potential and binding energies are calculated, but our result for the latter, i. e. B. E. =0, is not unique. The spectral shift of a light or neutrino ray to be received by an external observer is also analyzed, whose formula is an extension of our previous one in the case of gravitational collapse or anti-collapse with uniform density and negligible pressure.
理論物理学刊行会の論文
1967-07-25