Surface Tension and Negative Pressure Interior of a Non-Singular `Black
  Hole'
  The constant density interior Schwarzschild solution for a static,
spherically symmetric collapsed star has a divergent pressure when its radius
$R\le\frac{9}{8}R_s=\frac{9}{4}GM$. We show that this divergence is integrable,
and induces a non-isotropic transverse stress with a finite redshifted surface
tension on a spherical surface of radius
$R_0=3R\sqrt{1-\frac{8}{9}\frac{R}{R_s}}$. For $r < R_0$ the interior
Schwarzschild solution exhibits negative pressure. When $R=R_s$, the surface is
localized at the Schwarzschild radius itself, $R_0=R_s$, and the solution has
constant negative pressure $p =-\bar\rho$ everywhere in the interior $r<R_s$,
thereby describing a gravitational condensate star, a fully collapsed
non-singular state already inherent in and predicted by classical General
Relativity. The redshifted surface tension of the condensate star surface is
given by $\tau_s=\Delta\kappa/8\pi G$, where
$\Delta\kappa=\kappa_+-\kappa_-=2\kappa_+=1/R_s$ is the difference of equal and
opposite surface gravities between the exterior and interior Schwarzschild
solutions. The First Law, $dM=dE_v+\tau_s dA$ is recognized as a purely
mechanical classical relation at zero temperature and zero entropy, describing
the volume energy and surface energy change respectively. Since there is no
event horizon, the Schwarzschild time t of such a non-singular gravitational
condensate star is a global time, fully consistent with unitary time evolution
in quantum theory. The $p=-\bar\rho$ interior acts as a defocusing lens for
light passing through the condensate, leading to imaging characteristics
distinguishable from a classical black hole. A further observational test of
gravitational condensate stars with a physical surface vs. black holes is the
discrete surface modes of oscillation which should be detectable by their
gravitational wave signatures.
