Abstract
R- and T-regions of spacetime are first defined in a particular coordinate system and then with the aid of the Schwarzschild vacuum solution are shown to represent the outside and inside of a black hole respectively. A certain class of interior solutions, relating to a perfect fluid, are also considered and it is found that these R- and T-solutions have distinct physical properties. The R-solutions are static, spherically symmetric, permanent, and have a classical analogue, while the corresponding T-solutions, which are wholly time dependent, are cylindrical, temporary, and do not have a classical analogue. It is shown that these T-solutions cannot be generated from their R-region counterparts. Particular T-solutions are also presented in which the corresponding fluid occupies the whole of a T-region. The fluid would under certain circumstances be black body radiation while for other cases the internal pressure is always greater than the density.
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McVittie, G.C., Wiltshire, R.J. Fluid spheres and R- and T-regions in general relativity. Int J Theor Phys 14, 145–159 (1975). https://doi.org/10.1007/BF01807663
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DOI: https://doi.org/10.1007/BF01807663