Type D solutions of 3D new massive gravity

Ahmedov H., NUHBALAOĞLU A.

Physical Review D - Particles, Fields, Gravitation and Cosmology, cilt.83, sa.8, 2011 (SCI-Expanded, Scopus)

Özet

In a recent reformulation of three-dimensional new massive gravity, the field equations of the theory consist of a massive (tensorial) Klein-Gordon type equation with a curvature-squared source term and a constraint equation. Using this framework, we present all algebraic type D solutions of new massive gravity with constant and nonconstant scalar curvatures. For constant scalar curvature, they include homogeneous anisotropic solutions which encompass both solutions originating from topologically massive gravity, Bianchi types II, VIII, IX, and those of non-topologically massive gravity origin, Bianchi types VI0 and VII0. For a special relation between the cosmological and mass parameters, λ = m2, they also include conformally flat solutions, and, in particular, those being locally isometric to the previously-known Kaluza-Klein type AdS2×S1 or dS2×S1 solutions. For nonconstant scalar curvature, all the solutions are conformally flat and exist only for λ = m2. We find two general metrics which possess at least one Killing vector and comprise all such solutions. We also discuss some properties of these solutions, delineating among them black hole type solutions. © 2011 American Physical Society.