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 . 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 . For the interior Schwarzschild solution exhibits negative pressure. When , the surface is localized at the Schwarzschild radius itself, , and the solution has constant negative pressure everywhere in the interior , 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 , where is the difference of equal and opposite surface gravities between the exterior and interior Schwarzschild solutions. The First Law, is recognized as a purely mechanical classical relation at zero temperature and zero entropy, describing the volume energy and surface energy change respectively. 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. A clear observational test of gravitational condensate stars with a physical surface versus black holes is the discrete surface modes of oscillation which should be detectable by their gravitational wave signatures.