The author claims that Schwarzschild found that the vacuum solution to Einstein's equations predicted the existence of black holes with an event horizon. Nothing could be further from the truth! Schwarzschild found not one solution, but TWO solutions, termed "outer" and "inner" solutions. The inner solution contained matter; the Einstein energy-stress tensor was not zero, like in the outer solution. No mention of black holes was mentioned or even dreamed of.
Notwithstanding this, there are definite problems with the Schwarzschild solutions. Consider the outer solution. Gravity arises from an arbitrary constant of integration, resulting from the integration of the eigenvalues of the Ricci equations. This is hardly a dignifed way of accounting for gravity. The author claims that mass/energy deforms space/time. Yet, a mass arises from the constant of integration from the solution of Einstein's equations for an "empty" universe. This is certainly a glaring incompatibility.
General Relativity sees to transform forces into geometry. Yet, the geodesic equations predict the existence of forces. In the case of the Schwarzschild outer solution, it is Newton's inverse-square law of gravitation. So it is the existence of forces that distort space/time, and not the presence of mass/energy. Moreover, all terms appearing in the geodesic equations with zero external forces are fictitious forces which disappear in inertial frames. This would mean that gravity, too, is a fictitious force.
In summary this is nothing in the Schwarzschild solutions that would even hit at the existence of blackholes, gravistars, and nestars.
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