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Physical acceptability of isolated, static, spherically symmetric, perfect fluid solutions of Einstein’s equations. (English) Zbl 1002.83511
Summary: We ask the following question: Of the exact solutions to Einstein’s equations extant in the literature, how many could represent the field associated with an isolated static spherically symmetric perfect fluid source? The candidate solutions were subjected to the following elementary tests: (i) isotropy of the pressure, (ii) regularity at the origin, (iii) positive definiteness of the energy density and pressure at the origin, (iv) vanishing of the pressure at some finite radius, (v) monotonic decrease of the energy density and pressure with increasing radius, and (vi) subluminal sound speed. A total of 127 candidate solutions were found. Only 16 of these passed all the tests. Of these 16, only 9 have a sound speed which monotonically decreases with radius. The analysis was facilitated by use of the computer algebra system {\it GRTensorII}.

MSC:
83C15Closed form solutions of equations in general relativity
83C20Classes of solutions of equations in general relativity
83-08Computational methods (relativity)
Software:
GRTensorII
WorldCat.org
Full Text: DOI
References:
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