We find exact nonlinear solutions of general relativity that represent twisted gravitational waves (TGWs) in the presence of a cosmological constant. A TGW is a nonplanar wave propagating along a fixed spatial direction with a null Killing wave vector that has a nonzero twist tensor. The solutions all turn out to have wave fronts with negative Gaussian curvature. Among the classes of solutions presented in this paper, we find a unique class of simple conformally flat TGWs that is due to the presence of a negative cosmological constant and therefore represents part of anti–de Sitter spacetime. The properties of this special solution are studied in detail.

• Received 2 April 2019

DOI:https://doi.org/10.1103/PhysRevD.100.084027