HIGHER DIMENSIONAL TYPE N AND III SOLUTIONS OF EINSTEIN GRAVITY AND QUADRATIC GRAVITY

Abstract

We study exact vacuum solutions to Einstein gravity and quadratic gravity (QG) of the Weyl types N and III. We show that in an arbitrary dimension all Einstein spacetimes of the Weyl type N and a subclass of Einstein type III spacetimes are exact solutions to QG and we refer to explicitly known metrics within these classes. We also study a wider class of spacetimes admitting a pure radiation term in the Ricci tensor. In contrast to the Einstein case, the field equations of generic QG determine optical properties of the geometry and restrict such exact solutions to the Kundt class.