Matching the Kerr solution on the surface of a rotating perfect fluid
As it is known, nobody obtained till now the interior exact solution of Einstein's field equations for the Kerr metric. Therefore, any rigorous investigation of the Kerr-like matching conditions applying to the surface of a rotating perfect fluid is by far very important and can serve at least, like the authors say, ``to eliminate certain configurations of the surface for which one should not attempt to seek an interior solution''. Using the Boyer surface condition [\textit{R. H. Boyer}, Proc. Camb. Philos. Soc. 61, 527-530 (1965; Zbl 0127.182)], the authors perform a detailed analysis of the possible shapes of the surface of rotating perfect fluids on which the Kerr metric can be matched and summarize the results as follows. ``In the case of a rigidly rotating perfect fluid, it appears that the kidney-shaped toroidal surfaces, while yielding a vanishing pressure matching the Kerr metric, are not suitable candidates. Neither are strictly spheroid surfaces. When differential rotation is allowed for a perfect fluid, it appears from our considerations that it would be worth attempting to construct an interior solution for strictly spheroidal surfaces.'' With respect to the last statement, the authors point out that when the angular velocity is a single-valued function on the surface of the differentially rotating fluid, the equatorial acceleration is very similar to that observed on the surface of the sum and the angular velocity distribution is identical with the well-known Thorne's ``angular velocity of cumulative dragging''.
scientific article; zbMATH DE number 469174
scientific article