| Physical Acceptability of Exact Spherically Symmetric Perfect Fluid Solutions | |||||||||||||
| (this table updates all solutions listed as physically acceptable on the webpage | |||||||||||||
| http://grtensor.phy.queensu.ca/solutions/) | |||||||||||||
| Criteria: | |||||||||||||
| #1 - Isotropy of the Pressure | |||||||||||||
| #2 - Regularity of the origin | |||||||||||||
| #3 - The solution must remain "exact" after being matched continuously to a vacuum exterior. | |||||||||||||
| (In other words, an analytic solution of the Darmois-Israel junction conditions for the arbitrary constants appearing in the metric is known.) | |||||||||||||
| #4 - Finite and Positive Pressure and Energy Density | |||||||||||||
| #5 - Monotonically Decreasing Pressure and Energy Density | |||||||||||||
| #6 - Finite dp / drho | |||||||||||||
| #7 - dp / drho < 1 | |||||||||||||
| #8 - monotonically decreasing dp / drho | |||||||||||||
| Note: Tolman VII is the same as PV-Iia and Mehra (T=1), MW1 is the same as Finch-Skea | |||||||||||||
| For more information on the Tolman VII solution see www.astro.queensu.ca/~neary | |||||||||||||
| We have only provided parameter ranges for two-parameter solutions. | |||||||||||||
| (In all these, the boundary radius, R, scales the solution, and physical quantities are affected only by the tenuity, R/M. | |||||||||||||
| The Tolman IV family of solutions are denoted by (n=1,3,4,5,and n=1 extension) | |||||||||||||
| Metric | #1 | #2 | #3 | #4 | #5 | #6 | #7 | #8 | |||||
| Tolman IV (Tolman IV, n=1) | Y | Y | Y | R/M>3 | R/M>3 | R/M>3 | R/M>3 | N | |||||
| Heintz II-a (Tolman IV, n=3) | Y | Y | Y | R/M>2.65 | R/M>2.65 | R/M>2.65 | R/M>2.91 | 2.65<R/M<2.69 | |||||
| Durg IV (Tolman IV,n=4) | Y | Y | Y | R/M>2.70 | R/M>2.70 | R/M>2.70 | R/M>3.20 | 2.70<R/M<3.46 | |||||
| Durg V (Tolman IV, n=5) | Y | Y | Y | R/M>2.82 | R/M>2.82 | R/M>2.82 | R/M>3.50 | R/M>2.82 | |||||
| MW1 (Tolman IV, n=1 ext) | Y | Y | Y | R/M>2.52 | R/M>2.52 | R/M>2.52 | R/M>2.79 | 2.52<R/M<2.68 | |||||
| Wyman II-a | Y | Y (n=1, n=-1) | Y | N | |||||||||
| Buch I | Y | Y | N | ||||||||||
| Buch III | Y | Y | Y | R/M>5 | R/M>5 | R/M>5 | R/M>6 | R/M>5 | |||||
| Tolman VII (T=1) | Y | Y | Y | R/M>2.59 | R/M>2.59 | R/M>2.59 | R/M>3.71 | R/M>2.59 | |||||
| Gold III | Y | Y | Y | R/M>3.71 | R/M>3.71 | R/M>3.71 | R/M>4.68 | R/M>3.71 | |||||
| PS2 (3 parameter solution) | Y | Y | Y | Y | Y | Y | Y | Y | |||||
| Nariai IV | Y | Y | N* | ||||||||||
| Kuch2 III | Y | Y | Y | R/M>3.6 | R/M>3.6 | R/M>3.6 | R/M>6.43 | R/M>3.6 | |||||
| Whitman II | Y | Y | N | ||||||||||
| Whitman IV | Y | Y | N | ||||||||||
| * - more information to follow | |||||||||||||