On Fast Travel through spherically symmetric spacetimes

TL;DR

This paper investigates the limits of signal travel times in spherically symmetric spacetimes under energy conditions, showing they are constrained by Minkowski space times and exploring how energy conditions affect signaling speed.

Contribution

It proves a theorem relating signaling times in such spacetimes to Minkowski space and analyzes how different energy conditions influence these times.

Findings

Signaling times in weak energy condition spacetimes are no faster than in Minkowski space.

Stronger energy conditions may significantly slow down signal propagation.

Examples indicate that dominant energy condition restricts signaling speed more than weak energy condition.

Abstract

In a static spacetime, the Killing time can be used to measure the time required for signals or objects to propagate between two of its orbits. By further restricting to spherically symmetric cases, one obtains a natural association between these orbits and timelike lines in Minkowski space. We prove a simple theorem to the effect that in any spacetime satisfying the weak energy condition the above signaling time is, in this sense, no faster than that for a corresponding signal in Minkowski space. The theorem uses a ormalization of Killing time appropriate to an observer at infinity. We then begin an investigation of certain related but more local questions by studying particular families of spacetimes in detail. Here we are also interested in restrictions imposed by the dominant energy condition. Our examples suggest that signaling in spacetimes satisfying this stronger energy condition may be significantly slower than the fastest spacetimes satisfying only the weak energy condition.