93 research outputs found
All "static" spherically symmetric perfect fluid solutions of Einstein's equations with constant equation of state parameter and finite-polynomial "mass function"
We look for "static" spherically symmetric solutions of Einstein's Equations
for perfect fluid source with equation of state . In order to include
the possibilities of recently popularized dark energy and phantom energy
possibly pervading the spacetime, we put no constraints on the constant . We
consider all four cases compatible with the standard ansatz for the line
element, discussed in previous work. For each case we derive the equation
obeyed by the mass function or its analogs. For these equations, we find {\em
all} finite-polynomial solutions, including possible negative powers.
For the standard case, we find no significantly new solutions, but show that
one solution is a static phantom solution, another a black hole-like solution.
For the dynamic and/or tachyonic cases we find, among others, dynamic and
static tachyonic solutions, a Kantowski-Sachs (KS) class phantom solution,
another KS-class solution for dark energy, and a second black hole-like
solution.
The black hole-like solutions feature segregated normal and tachyonic matter,
consistent with the assertion of previous work. In the first black hole-like
solution, tachyonic matter is inside the horizon, in the second, outside.
The static phantom solution, a limit of an old one, is surprising at first,
since phantom energy is usually associated with super-exponential expansion.
The KS-phantom solution stands out since its "mass function" is a ninth order
polynomial.Comment: 24 standard LaTeX pages, 4 tables, no figures. -Title changed to
avoid equation in title. -The set of solutions and their interpretation
remains unchanged, but new classification of solutions (solution labels also
changed), consolidation of appendix into a table (omitting calculation
details) resulted in shorter paper. -Updated Publication info for preprints
in Reference
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