Timelike curves of limited acceleration in general relativity

Abstract

A simple result, restricting the behavior of a timelike curve under limitations on its integrated acceleration, is obtained and discussed.

Optimal time travel in the Gödel universe

“…again by the isoperimetric property of the circle (an equivalent observation was made in [3]). Choosing the natural orthonormal frame…”

On efficient “time travel” in Gödel spacetime

“…Our result turns on the fact that closed timelike curves are not required to be smooth everywhere: at the initial (=terminal) point a "kink" is permitted. 3 Physically, an observer traveling along a kinked closed timelike curve γ : [s i , s f ] → M in a spacetime (M, g ab ) will have different initial and final velocity vectors ξ a i and ξ a f at the point γ (s i ) = γ (s f ). Of course, since the time traveler cannot, at this kink point, instantaneously switch from ξ a f back to ξ a i (that would imply an infinite acceleration) this means that the trip cannot be immediately repeated.…”

“…Here, we will focus on a small handful of classical questions concerning total acceleration efficiency along closed timelike curves [3,[12][13][14].…”

“…So the second question, posed by Chakrabarti, Geroch, and Liang [3], is this: (Q2) Is there some number k > 0 such that, for all closed timelike curves γ in Gödel spacetime, T A(γ ) ≥ k? Malament [12] showed there is indeed such a number: ln(2 + √ 5) will do.…”

On the Possibility of Supertasks in General Relativity

“…Given such examples, Earman and Norton demand a finite bound on the total acceleration of γ. This seems sensible -a rocket ship which carries a finite amount of fuel cannot traverse a curve with infinite total acceleration (assuming it cannot refuel along the way) [1]. So, we have the following.…”