Causality is one of the most important properties to understand gravity theories. It gives us not only a method to confirm that the gravity theories are really consistent, but also gives implications about the properties which unknown fundamental physics should obey. We investigate the causality of three-dimensional (3D) gravity theories, which are considered to be important, by using the Shapiro time delay effect in the Shock wave geometry. One of such gravity theories is the Zwei-Dreibein Gravity (ZDG) theory, which is a consistent 3D gravity theory. In ZDG theory, the serious problems can be removed that have appeared in another important gravity theory called New Massive Gravity (NMG). We study whether the ZDG theory could preserve the causality without losing the above good properties and how the causality structure is related to the structure of the NMG theory.
Complexity-action duality of the shock wave geometry in a massive gravity theory
