What is faster -- light or gravity?

TL;DR

This paper introduces the concept of superluminal and semi-superluminal alternatives to define and analyze the speed of gravity within general relativity, concluding that such superluminal signals are absent under certain conditions.

Contribution

It formalizes the notions of superluminal and semi-superluminal alternatives to address the speed of gravity in general relativity and proves their absence in globally hyperbolic spacetimes.

Findings

Superluminal alternatives are absent in general relativity under certain conditions.

Semi-superluminal alternatives are also absent in constrained spacetimes.

The paper clarifies the conceptual understanding of gravitational signal speed.

Abstract

General relativity lacks the notion of the speed of gravity. This is inconvenient and the present paper is aimed at filling this gap up. To that end I introduce the concept of the "alternative" and argue that its variety called the "superluminal alternative" describes exactly what one understands by the "superluminal gravitational signal". Another, closely related, object called the "semi-superluminal alternative" corresponds to the situation in which a massive (and therefore gravitating) body reaches its destination sooner than a photon \emph{would}, be the latter sent \emph{instead} of the body. I prove that in general relativity constrained by the condition that only globally hyperbolic spacetimes are allowed 1) semi-superluminal alternatives are absent and 2) under some natural conditions and conventions admissible superluminal alternative are absent too.