Causality in 3D massive gravity theories

Abstract

We study the constraints coming from local causality requirement in various 2 + 1 dimensional dynamical theories of gravity. In topologically massive gravity, with a single parity non-invariant massive degree of freedom, and in new massive gravity, with two massive spin-2 degrees of freedom, causality and unitarity are compatible with each other and both require the Newton's constant to be negative. In their extensions, such as the Born-Infeld gravity and the minimal massive gravity the situation is similar and quite different from their higher dimensional counterparts, such as quadratic (e.g., Einstein-Gauss-Bonnet) or cubic theories, where causality and unitarity are in conflict. We study the problem both in asymptotically flat and asymptotically anti-de Sitter spaces.

Exotic massive gravity: Causality and a Birkhoff-like theorem

“…It pays to reproduce end extend the results of the above computation-done for null geodesicsto fields following [17]. In particular, the results become more transparent for a massless scalar field (still a test field with no back reaction) propagating in the background shock-wave.…”

“…But this cannot be done with a single chart for the whole spacetime, so, one can choose the y > 0 part to be asymptotically flat in the Cartesian form. For more discussion on this issue, see [17,25]. A careful analysis leads to the following metric profile function with all arbitrary parameters fixed:…”

“…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 antide 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 moreover addition of finite number of curvature terms in the theory does not solve the problem.…”

“…As discussed in [17], the usual computation of the Shapiro time delay of a signal is done for a round trip in a black hole background for more than three spacetime dimensions. However, in three dimensions, using the motion of test particles or fields in a shockwave geometry [20,21] created by a massless particle is better suited.…”

Impulsive gravitational waves in general massive 3D gravity

“…In a more recent work [34], introducing impulsive gravitational waves generated by null particles in three spacetime dimensions [35], it has been shown that the local causality and unitarity (the absence of ghosts and tachyons at the linearized level) are not in conflict in flat and AdS backgrounds for massive gravity models.…”