Surface Tension and Negative Pressure Interior of a Non-Singular `Black Hole'

Abstract

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, $dM=d{E}_v+{\tau }_{s}dA$ 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.

45 pages, 10 figures, Dedicated to Professor Andrzej Staruszkiewicz on the occasion of his 75th birthday

References in corpus (5)

• How to tell a gravastar from a black hole
• Cosmological Dark Energy: Prospects for a Dynamical Theory
• Can accretion disk properties distinguish gravastars from black holes?
• Gravastar Shadows
• Macroscopic Effects of the Quantum Trace Anomaly

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