Abstract
We study the local causality issue via the Shapiro time-delay computations in the on-shell consistent exotic massive gravity in three dimensions. The theory shows time-delay as opposed to time-advance despite having a ghost at the linearized level both for asymptotically flat and anti-de Sitter spacetimes. We also prove a Birkhoff-like theorem: any solution with a hypersurface orthogonal non-null Killing vector field is conformally flat; and find some exact solutions.
Highlights
Three-dimensional spacetime is poor in massless gravitons, yet very rich in massive ones: in addition to the well-known topologically massive gravity (TMG) [1], new massive gravity (NMG) [2], cubic [3], and Born-Infeld extensions [4], which are all based on actions that depend on the metric alone, a new set of theories that lack a purely metric-based action have been found in [5,6,7]
Following the discussion of causality of extended gravity theories in [16,17] using the Shapiro time-delay computation [18], we study the causality of exotic massive gravity” (EMG) both in asymptotically flat and anti–de Sitter (AdS) spacetimes
In addition to the causality discussion, we prove a theorem which is in some sense analogous to the Birkhoff theorem in four dimensions: all solutions of EMG that possess a hypersurface orthogonal non-null Killing vector field are conformally flat
Summary
Three-dimensional spacetime is poor in massless gravitons, yet very rich in massive ones: in addition to the well-known topologically massive gravity (TMG) [1], new massive gravity (NMG) [2], cubic [3], and Born-Infeld extensions [4], which are all based on actions that depend on the metric alone, a new set of theories that lack a purely metric-based action have been found in [5,6,7]. Following the discussion of causality of extended gravity theories in [16,17] using the Shapiro time-delay computation [18], we study the causality of EMG both in asymptotically flat and anti–de Sitter (AdS) spacetimes. It was realized in [16] that the Einstein-Gauss-Bonnet theory is not causal even in the regime when the theory is unitary and the addition of finite number of curvature terms in the theory does not solve the problem. V, we show that the solutions of TMG are inherited by EMG as long as the coupling parameters of the theories are related in a prescribed way
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