On Fast Travel through spherically symmetric spacetimes

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.