Einstein's general relativity geometrizes the gravitational field. Since it is no longer a field of force how can it contain, no less conserve, mass-energy? As long as we are working in Euclidean space, conservation is expressed as the vanishing of a divergence. Only for Cartesian components of Euclidean space are the components of a tensor independent of the space point to which the tensor is connected to. This is no longer true for curvilinear coordinates even in Euclidean space, let alone for non Euclidean geometries.
Had Maxwell been a contemporary of Einstein how would he have reacted to his general theory of relativity? Einstein's theory makes the very mistake that so bothered Maxwell that he "gave gravity up as beyond 19th century physics."
The perennial question as to whether a charge in a uniform gravitational field would radiate has seen its comeback many times. Looking at gravity as a force from the special relativitic viewpoint it would appear that the answer is "yes", but considering gravity as geometry from a general relativistic perspective one would be or inclined to say "no", which is what Bondi and Gold claimed.
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.