Causality in 3D massive gravity theories

We study the constraints coming from the local causality requirement in various $2+1$ dimensional dynamical theories of gravity. In topologically massive gravity, with a single parity noninvariant 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.

Figure 1

Integration contours in the complex $q$-plane depending upon the sign of the impact parameter $b$, this prescription corresponding to the gauge choice $c_1(u)=2|p|\delta (u)$ and $c_2(u)=0$.