| dc.description |
We develop a model for the gravitational field which is renormalizable, conformally invariant and integrable in four dimensions. The first two conditions can be easily implemented. However, for the latter condition we must take recourse to fourth-rank geometry where the line element is defined by a quartic form, . The simplest Lagrangian which can be constructed in this case depends quadratically on a Ricci tensor constructed only in terms of a connection; therefore a Palatini-like variational principle is applied. The field equations imply that the fourth-rank metric decomposes into a product of a second-rank metric with itself, and in this case the geometry becomes Riemannian. The decomposition of the fourth-rank metric means our field equations become linear in the Ricci tensor and thus they are amenable for comparison with the Einstein field equations. We show that the Einstein field equations are a particular case of our field equations. The field equations are solved in the spherically symmetric case. The solution contains the Schwarzschild metric and the Kottler metric, corresponding to a massive point particle on a Minkowski and a de Sitter background, respectively. |
