In a New York Times science article entitled "A scientist takes on gravity" (July 12th, 2010) Verlinde claims "that gravity is a consequence of the venerable laws of thermodynamics which describe the behavior of heat and gases." Continuing we read "gravity is simply a byproduct of nature's propensity to maximize disorder." The analogy with 'hair fizzles' couldn't be more adapt: it actually makes your hair want to stand up straight!
Even before the appearance of Einstein's definitive paper on the General Theory of Relativity, Schwarzschild solved Einstein's equations on the assumptions that the space was empty, and that light rays could arrive and depart from a central point mass. Furthermore, it was assumed to be differentiable everywhere.
In a recently published book, "Reflections on Relativity", Kevin Brown (which has been on the internet for several years) derives the Schwarzschild metric from Kepler's third law without recognizing that it violates Kepler's second law. In fact, the violation of Kepler's second law is necessary in order to derive the deflection of light about a massive body and the precession of elliptical orbits.
The putative cosmological singularities that lead to black holes via the Schwarzschild metric, and the big bang via the Robertson-Walker line element, are consequences of extending the cosmological models beyond their domain of validity, or simply incorrect to begin with.
In 1934 Milne and McCrea [Quart. J. Math. 5 (1934) 73-80] made a startling discovery that still is not fully resolved. In Harrison's [Cosmology (Cambridge U. P., 2000), 2nd ed. p.326] words: "Why should Newtonian theory and general relativity, when applied to a uniform universe, yield identical results? At best, Newtonian theory is only approximately true, and yet in this most unlikely of all applications it gives the correct result." Milne and McCrea derived the Friedmann-Lemaitre equations for the expansion rate of the universe at zero pressure.
Cosmologists confuse first and second order phase transitions. They are, in fact, mutually exclusive. What is even worse is that if the early universe was expanding adiabatically, the product of the radius and temperature is an adiabatic invariant. In the two phase region the volume can be changed without changing the pressure. The pressure is a sole function of the temperature. The adiabatic condition destroys all this, and, hence, there can be no latent heat of condensation or evaporation.
In a paper on negative heat capacities [Mon. Not. R. ast. Soc. 181 (1977), 405-419] Lynden-Bell and Lynden-Bell claim that "All astronomers know that when a star or a star cluster loses energy its temperature will increase in accordance with the virial theorem. Beckenstein [sic] & Hawking have demonstrated that black holes display the same phenomenon. Thus astronomical systems display negative specific heat." Then all astronomers would be wrong.
It has long been observed that the pressure enters Einstein’s equations with the wrong sign. It would tend to increase the mass of a gravitating body rather than acting to oppose gravitational collapse. In other words, stellar equilibrium is maintained by an interior pressure that balances exactly the force of gravity, and, therefore, it cannot contribute to the mass it is trying to oppose from collapsing.