1.a GR as a field theory and Alternative Theories of Gravity

This line involves a close examination of the theories of Gravitation. The main idea can be described as follows. In the begining of the 60's, Gupta, Feynmann and others showed that it is possible to describe all the properties of Einstein's General Relativity without the use of the geometrical representation, but applying instead the usual tools of Field Theory. Several authors since then have examined this field formulation of Gravitation, and we have nowadays a more or less complete list of its classical and quantum properties. As an example, we can cite the work of Deser in 1970, and more recently, a revision of that work by Grischuck, Petrov e Popova (1984).

The importance of this formulation lies in the fact that it succeded in exhibiting some properties of the gravitational field that were hidden, so to say, in the geometric representation presented by Einstein. A particularly important property among these is the Equivalence Principle. In a simple way, we can say that this principle states that every form of matter and radiation (for instance photons) interacts in the same unique way with gravitation. It is often said that this hypothesis has been tested up to a level of one part in 1011. However, we do not have yet any experiment that tests the interaction of the gravitational energy with gravity itself.

In General Relativity, it is assumed that the interaction of gravitation with itself follows the same principle. The greatest achievement of Feynmann and Deser's formulation was precisely to explicit this hypothesis, that extends the range of the Equivalence Principle further away from the observational limits available. If we simply assume that gravitation does not couple to gravitational energy following the Equivalence Principle, we obtain an alternative theory, competitive with Einstein?s General Relativity. Several predictions of this new theory, elaborated by our group, are radically different from those of GR. The main difference between the two theories is in the prediction of the velocity of propagation of gravitational waves. If we take into account that soon we will have at our disposal observations of gravitational waves, it is of crucial importance to have alternative scenarios available to interpret the results of the observations. The research plan we propose in this line includes:

  1. Detailed study of the properties and solutions of this new field theory of gravitation related to compact and cosmological sources.
  2. Hamiltonian Formulation
  3. Canonical Quantization
  4. The problem of gravitational energy in this theory.
  5. Detailed analysis of gravitational waves in this theory, and specific predictions to be compared with future observations.
A specific lagrangian for this new theory was presented in M.Novello, L.R.de Freitas e V.A.De Lorenci, Annals of Physics 254, 83, 1997. We showed that the PPN parameters of the theory are in agreement with those of GR, and consequently the theory agrees with solar system observations. In fact, the differences are evident only in the strong field regime, and in the propagation of gravitational waves. We also studied the latter item, showing that the predictions of our theory drastically differ from those of GR. We are now proceeding with this avenue of research, with the study of the radiation emitted by the binary pulsar in the light of our theory (christened NDL theory), in the post-newtonian approximation, with the quadrupole formula.

It is important to remark that the detection of gravitational waves has become one of the most important quests of research in gravitation. According to GR, the discontinuities in the gravitational field must propagate with the velocity of the electromagnetic waves. This is a desirable property, in the sense that corresponds to a unified causal structure. The distinguishing feature of NDL theory is that the propagation of gravitational waves has a velocity different from the velocity of light. We must wait until LIGO and the other observatories are collecting data for this question to be settled.