Scattering amplitudes in high-energy limit of projectable Hořava gravity

We study the high-energy limit of projectable Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity using on-shell graviton scattering amplitudes. compute tree-level amplitudes symbolic computer algebra and analyze their properties in case collisions with zero total momentum. The grow collision energy way consistent unitarity. discuss angular dependence derive expression for differential cross section that happens to depend only on essential combinations couplings. One our key results is arbitrary kinematics are finite when coupling $\ensuremath{\lambda}$ kinetic Lagrangian taken infinity---the value corresponding candidate asymptotically free ultraviolet fixed points theory. formulate a modified action which reproduces same directly applicable at $\ensuremath{\lambda}=\ensuremath{\infty}$, thereby establishing $\ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$ regular. As an auxiliary result, we generalized Ward identities nonrelativistic gauge theories.