Particle content and degrees of freedom of a gravitational field in 4 th order theories of gravity

In gravitational theories of 4‐th order, the influence of certain properties of the field equations (tracelessness, conformal invariance, scale in variance respectively their breaking) for the “particle content” (number of degrees of freedom, mass, spin) is investigated. Using the plane‐wave ansatz valid in linearized theory it is possible to determine the mass content of the theory, but one cannot get assertions about the number of degrees of freedom and the spin states corresponding to the field quanta. In the linearized theory, this can be done with a spin projection formalism. Using the Cauchy initial value problem and a counting method first developed by EINSTEIN one can get, however, a useful definition of the concept of the degrees of freedom for the full nonlinear theory. This is due to the fact that this method allows to incorporate the concrete structure of the field equations (and thus their nonlinearities). Analysing different general‐relativistic field theories via these approaches the influence of the various structures of nonlinearities is discussed. It is, in particular, shown that those results obtained by the spin projection formalism can be reproduced by “nonlinear methods”.