1998/09/02 by M. S. R. Delgaty, M.S.R. Delgaty, Kayll Lake · 1 voice · 645 citations
Engineering · Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Energy (signal processing) #Energy density #Extant taxon #Fluid dynamics and aerodynamics studies #Isotropy #Monotonic function #Navier-Stokes equation solutions #Perfect fluid #Positive definiteness #Speed of sound #astro-ph #gr-qc
paper · pdf · doi:10.1016/s0010-4655(98)00130-1
published in Computer Physics Communications 115(2-3), 395-415 (Elsevier BV) · 25 pages. To appear in Computer Physics Communications Thematic Issue on "Computer Algebra in Physics Research"
arxiv created 1998/09/02 · arxiv published 1998/09/02 · arxiv updated 1998/09/02 · openalex publication_date 1998/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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 GRTensorII.