Homogeneous anisotropic solutions of topologically massive gravity with a cosmological constant and their homogeneous deformations

We solve the equations of topologically massive gravity with potentially non-vanishing cosmological constant for homogeneous metrics without isotropy. We only reproduce known solutions. We also discuss their homogeneous deformations, possibly with isotropy. We show that de Sitter space and hyperbolic space cannot be infinitesimally homogeneously deformed in TMG. We clarify some of their Segre-Petrov types and discuss the warped de Sitter spacetime.
latex, 56 pages, pdf figures, tikz figures. v3: corrected deformation graph, added discussion on de Sitter / hyperbolic deformation, typo corrections, more notation crossrefs, changed so(theta) to iso(theta) notation, a few more refs, publication version, no major changes