Dear Christian,
I agree with you that general relativity (GR) is perfect theory which give us exact results. But the problem with GR is connected with the methodology of physics itself and with the fundamentals of the theory. To make the situation more clear let take the next example. Suppose we have a steady flow of an incompressible liquid with a constant flow rate through the tube which has a variable cross-section S, in the absence of gravitational forces. If [math]\rho[/math] is the density of the liquid, V is the average speed of the flow, then the formula for the mass flux is: [math]\rho V S=const =C[/math] When the section S is changing the speed V of the liquid and the density of the kinetic energy Ek in this section is changed: [math]E_k=\frac {\rho V^2} {2}= \frac {C^2} {2 \rho S^2}[/math] In this case the density of the kinetic energy is inextricably linked with the geometry, and we can write the law of conservation of energy density [math]E_k + f(S)= const [/math] where [math]f(S)[/math] is a geometric function of the cross section S, which in general can arbitrarily depend on external conditions affecting S. On the other hand, we can do not use the geometry, and consider the potential energy of the liquid in the form of pressure P, then the sum of the kinetic and the potential energy will be saved regardless of S: [math]E_k +P= const [/math] This shows that the problem with pseudotensor energy field arises in general relativity because of the fact that there the role of energy is performed by geometric quantities, and the gravitational field itself is reduced to the metric field and the curvature of spacetime. Of course, gravity changes the movement and energy of photons, which are used for the spacetime measurements. Hence the conclusion that the metric tensor in the presence of gravity changes its form relative to the metric of Minkowski space in the special theory of relativity. Therefore, such a change in GR metrics associated with gravity so as to satisfy the principle of equivalence. But then in GR energy-momentum tensor of the gravitational field disappear, and the field itself is not a real physical field but the geometrical object. Hence, there are paradoxes. For example in GR contribution to the gravitational field can make any other field, but the gravitational field itself do not make similar in the form of contributions in other fields. Then, why the gravitational field has such unique status? Because of the geometrization of the field in general relativity, we may never know exactly what causes spacetime to curve near the masses? And what is the maximum extent of this spacetime distortion? And where is the evidence that the degree of curvature is able to achieve the status of a black hole? Some of these problems are solved in the Covariant theory of gravitation. In this theory, gravitation exists as a fundamental physical field and has its own energy-momentum tensor like the electromagnetic field. That's gravitational field affects the movement and energy of photons or other test particles, and thus changes the spacetime metric, found by these photons and particles. The role of geometry is reduced only to a change in the metric by gravitation. At the same time as the physical mechanism of gravitation provides a mechanism in the Le Sage theory of gravitation, i.e. gravitation is a consequence of the fluxes of gravitons. And we can find density of energy of gravitons fluxes (http://vixra.org/abs/1209.0076).
Sergey Fedosin