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

TL;DR

This paper develops a method to construct and analyze black hole solutions in higher-dimensional gravity theories with superposed Gauss--Bonnet terms, providing explicit metrics, horizons, and maximal extensions, including effects of cosmological constant and charge.

Contribution

It introduces an iterative combinatorial approach to build higher-dimensional p-Riemann forms and derives explicit black hole metrics with maximal extensions in Gauss--Bonnet gravity.

Findings

Explicit black hole metrics with horizons derived from polynomial equations

Maximal Kruskal extensions constructed explicitly in general dimensions

Inclusion of cosmological constant and charge in higher-dimensional solutions

Abstract

Our starting point is an iterative construction suited to combinatorics in arbitarary dimensions d, of totally anisymmetrised p-Riemann 2p-forms (2p\le d) generalising the (1-)Riemann curvature 2-forms. Superposition of p-Ricci scalars obtained from the p-Riemann forms defines the maximally Gauss--Bonnet extended gravitational Lagrangian. Metrics, spherically symmetric in the (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 Euclidean signature. We show how to include a cosmological constant and a point charge. Possible further developments and applications are indicated.