We present solutions of the Einstein equations that extend the static Schwarzschild solution in empty space into regions of non-zero energy density ⍴ and radial pressure 𝑝 = 𝑤 ⍴, where 𝑤 is a constant equation of state parameter. For simplicity we focus mainly on solutions with constant ⍴. For 𝑤 = 0 we find solutions both with and without a singularity at the origin.   Possible applications to galaxies are considered, where we find enhanced velocity rotation curves towards the edge of a galaxy. We propose that our explicit  non-singular solution with 𝑤 = -1 describes the interior of a black hole,  which is a form of vacuum energy. We verifythat its entropy is consistent with the Bekenstein-Hawking entropy, if one assumes the Hawking temperature. We  further suggest that this idea can perhaps be  applied to the dark energy of the observable universe, ifone views the latter  as arising from  black holes as  pockets of vacuum energy. We estimate the averagedensity of such a dark energy to be approximately 1E-30 g/cm^3. We also speculate on applications to early time inflation.