Solutions of massive gravity theories in constant scalar invariant geometries (Q2843858)

Theories of gravity and its quantization in 3 space-time dimensions are under discussion as toy models for theories of gravity and its quantization in 4 space-time dimensions already over a long period of time. Nowadays, additionally, the purely classical (i.e. non-quantum) theories of gravity in 3 space-time dimensions enjoy much interest, too. This is the goal of the present paper: For such theories with Chern-Simons Lagrangian, Einstein-Hilbert Lagrangian, and new massive gravity related to the Lagrangian \(R_{ij} R^{ij} - 3 R^2 /8 \), they present several solutions in closed form and discuss their properties, e.g. from the Petrov classification's and from the constant scalar invariant (CSI) geometries points of view.