Gravitation with superposed Gauss-Bonnet terms in higher dimensions: Black hole metrics and maximal extensions

Our starting point is an iterative construction suited to combinatorics in arbitarary dimensions d, of totally anisymmetrized p-Riemann 2p forms (2p<~d) generalizing the (1-)Riemann curvature 2-forms. The superposition of p-Ricci scalars obtained from the p-Riemann forms defines the maximally Gauss-Bonnet extended gravitational Lagrangian. Metrics, spherically symmetric in (d-1) space dimensions, are constructed for the general case. The problem is directly reduced to solving polynomial equations. For some black-hole type metrics the horizons are obtained by solving polynomial equations. Corresponding Kruskal-type maximal extensions are obtained explicitly in complete generality, as is also the periodicity of time for the Euclidean signature. We show how to include a cosmological constant and a point charge. Possible further developments and applications are indicated.