Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-10-03
Rev.Math.Phys.23:865-882,2011
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
24 standard LaTeX pages, 4 tables, no figures. -Title changed to avoid equation in title. -The set of solutions and their inte
Scientific paper
10.1142/S0129055X1100445X
We look for "static" spherically symmetric solutions of Einstein's Equations for perfect fluid source with equation of state $p=w\rho$. 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 $w$. 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.
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