Effective speed approach for scalar field propagation

Abstract

We study the propagation of a constant speed gaussian scalar field wave-packet (GWP) in Minkowski space, showing that the energy conditions are violated for superluminal speed. We then apply the effective speed approach to the GWP propagation, deriving the corresponding effective metric, effective Lagrangian and effective stress-energy tensor, showing that the null, weak and strong energy conditions are satisfied.

Figures (2)

• Figure 1: The quantity $S$ is plotted as a function of $r$, for $\alpha = 1.1$, $\beta = \beta_m+10^{-6}$, $t = 10 \sigma/c$ and $n_r = -1$.
• Figure 2: The discriminant $\Delta$ is plotted as a function of $\beta$ and $n_r$.