Cauchy constraints and particle content of fourth-order gravity in \(n\) dimensions. (Q1419099)

The full class of purely metrical gravitational theories in \(n\geq 3\) dimensions which follows from a Lagrangian composed of linear and quadratic curvature ters is analyzed. The type of the field equations is discussed in a suitable gauge. The principal symbol and the particle content of the linearized field equations are investigated. The space+time decomposition and the ADM formalism are used to derive the constraints and evolution equations for the variational derivative tensor. However, the paper contains several errors for the case \(n=3\). Example 1: In the Corollary to Theorem 2.1., the phrase ``iff \(n=4\)'' has to be replaced by ``iff \(n=3\) or \(n=4\)'', to get a valid statement. Example 2: Theorem 3.8. is not valid for the case \(n=3\) due to the fact that in 3 dimensions, the Riemann tensor is a linear combination of products of the Ricci tensor with the metric. This leads to more restrictions to the particle content of the corresponding theory in 3 dimensions. These inaccuracies do not prevent this paper to be a quite useful one, as for physical applications, the case \(n=3\) is excluded anyhow.