Velocity of signal in attractive potential and propagation of light in gravitational field

TL;DR

This paper investigates how signals propagate in attractive potentials, demonstrating that wave fronts always move at light speed despite superluminal group velocities, with implications for light in gravitational fields.

Contribution

It clarifies that wave fronts in gravitational fields propagate at light speed, refuting recent claims of superluminal signal transmission in such contexts.

Findings

Wave front speed equals the speed of light.

Group velocity can exceed light speed without violating causality.

Wave packet deformation occurs with superluminal group velocities.

Abstract

The propagation of a massless field in attractive and repulsive potentials is considered. It is shown that though the group velocity in such potentials can be larger than one, the wave front propagates with the speed of light. A larger-than-one group velocity leads only to a strong deformation of the wave packet. The results obtained are applied to the light propagation in a gravitational field. An erroneous assertion concerning the last problem, recently made in the literature, is refuted.