Ten-dimensional Lovelock-type space-times

Abstract

The correct field equations for several ten-dimensional Lovelock-type Lagrangians including terms up to fourth order in the curvature are given. They were deduced from a program which exploits the facilities of the differential package EXCALC. A first discussion of the obtained equations is presented. The justification of a conjecture made recently by Deruelle is given. Possible extensions of some previously obtained solutions of the field equations restricted to quadratic and cubic contributions are discussed. Finally, some errors in the existing literature are pointed out.