The Cornell University , USA

**Abstract:**

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 verify that 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, if one views the latter as arising from black holes as pockets of vacuum energy. We estimate the average density of such a dark energy to be ρ ？_？e≈〖10〗^(−30) g∕cm^3. We also speculate on applications to early time inflation.

**Brief CV of Prof. Andre LeClair:**

Prof. Andre’ LeClair obtained a degree in physics from MIT in 1982, and a PhD from Harvard in 1987. After a postdoc at Princeton, he joined the faculty at Cornell University in the physics department, where he has been a full professor since 2001. He has received an Alfred P. Sloan Foundation Fellowship and a National Young Investigator award from the National Science Foundation. He has written over 115 articles in a broad range of topics, including string theory, Integrable quantum field theory, condensed matter theory, topological insulators, the Riemann Hypothesis, and more recently on black holes.

**联系人**：傅琦（82649469）