All "static" spherically symmetric perfect fluid solutions of Einstein's equations with constant equation of state parameter and finite-polynomial "mass function"

Understand

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.