Effective speed approach for scalar field propagation

TL;DR

This paper investigates scalar field wave-packet propagation at constant speed, demonstrating energy condition violations at superluminal speeds and deriving an effective metric that satisfies energy conditions.

Contribution

It introduces an effective speed approach and derives effective geometric quantities ensuring energy conditions are met for scalar wave propagation.

Findings

Superluminal scalar wave-packets violate energy conditions.

Effective metric and stress-energy tensor satisfy all classical energy conditions.

The approach provides a consistent framework for scalar wave propagation analysis.

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.