The Rocket Problem in General Relativity

Henriques, Pedro; Natário, José

doi:10.1007/s10957-012-0023-8

Cited by 9 publications

(15 citation statements)

References 11 publications

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“…In [8] the classical Newtonian theory of optimal rocket trajectories developed in [9] was generalized to the general relativity setting. There it is shown that optimal trajectories are expected to be continuous, sectionally smooth timelike curves, obtained by piecing together free-fall (geodesic) and accelerated arcs, possibly with instantaneous (Dirac delta) accelerations at the junction points.…”

Section: The Rocket Problem In General Relativitymentioning

confidence: 99%

“…Finally, it is easily seen from [8] that if the initial or final four-velocities are not specified then we must have P = 0 at those points. For free-fall arcs (a = 0), conditions (1) reduce to the geodesic and Jacobi (geodesic deviation) equations, with the first integrals (2) requiring the Jacobi field P to be orthogonal to the four-velocity U .…”

Section: The Rocket Problem In General Relativitymentioning

confidence: 99%

“…Gödel himself remarked that if the acceleration is provided by a rocket then the required amount of fuel is prohibitively high [5,12,15]. This amount can be computed from the well known rocket equation [1,8], which relates the initial and final rest masses of the rocket:…”

Section: Introductionmentioning

confidence: 99%

“…The candidate curve is more complicated than one would guess from the Euclidean space analogy, and is obtained by applying the general theory of optimal rocket trajectories in general relativity developed in [8]. For the reader's convenience, this theory is summarized in Sect.…”

Section: Introductionmentioning

confidence: 99%

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Optimal time travel in the Gödel universe

Natário¹

2011

Gen Relativ Gravit

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Using the theory of optimal rocket trajectories in general relativity, recently developed in Henriques and Natário (2011), we present a candidate for the minimum total integrated acceleration closed timelike curve in the Gödel universe, and give evidence for its minimality. The total integrated acceleration of this curve is lower than Malament's conjectured value (Malament 1984), as was already implicit in the work of Manchak (Gen. Relativ. Gravit. 51-60, 2011); however, Malament's conjecture does seem to hold for periodic closed timelike curves.

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Section: The Rocket Problem In General Relativitymentioning

confidence: 99%

Section: The Rocket Problem In General Relativitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal time travel in the Gödel universe

Natário¹

2011

Gen Relativ Gravit

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“…[10] derived the optimality conditions for rocket trajectories in general relativity, though it was done from an analytical approach and did not consider any specific trajectories. To date, very little research has been performed on optimising interstellar 40 trajectories in a general relativistic framework.…”

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confidence: 99%

The optimisation of low-acceleration interstellar relativistic rocket trajectories using genetic algorithms

Fung

Lewis

2017

Acta Astronautica

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A vast wealth of literature exists on the topic of rocket trajectory optimisation, particularly in the area of interplanetary trajectories due to its relevance today. Studies on optimising interstellar and intergalactic trajectories are usually performed in flat spacetime using an analytical approach, with very little focus on optimising interstellar trajectories in a general relativistic framework. This paper examines the use of low-acceleration rockets to reach galactic destinations in the least possible time, with a genetic algorithm being employed for the optimisation process. The fuel required for each journey was calculated for various types of propulsion systems to determine the viability of low-acceleration rockets to colonise the Milky Way. The results showed that to limit the amount of fuel carried on board, an antimatter propulsion system would likely be the minimum technological requirement to reach star systems tens of thousands of light years away. However, using a low-acceleration rocket would require several hundreds of thousands of years to reach these star systems, with minimal time dilation effects since maximum velocities only reached about 0.2c. Such transit times are clearly impractical, and thus, any kind of colonisation using low acceleration rockets would be difficult. High accelerations, on the order ✩ Corresponding author.Email address: kfun2342@uni.sydney.edu.au, geraint.lewis@sydney.edu.au, xiaofeng.wu@sydney.edu.au (Kenneth K H Fung ✩,a,b , Geraint F Lewis a , Xiaofeng Wu b ) Preprint submitted to Acta Astronautica February 2, 2017 of 1 g, are likely required to complete interstellar journeys within a reasonable time frame, though they may require prohibitively large amounts of fuel. So for now, it appears that humanity's ultimate goal of a galactic empire may only be possible at significantly higher accelerations, though the propulsion technology requirement for a journey that uses realistic amounts of fuel remains to be determined.

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Optimal Time Travel in the Gödel Universe

Natário¹

2013

Springer Proceedings in Mathematics &Amp; Statistics

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Using the theory of optimal rocket trajectories in general relativity, recently developed in [HN11], we present a candidate for the minimum total integrated acceleration closed timelike curve in the Gödel universe, and give evidence for its minimality. The total integrated acceleration of this curve is lower than Malament's conjectured value [Mal84], as was already implicit in the work of Manchak [Man11]; however, Malament's conjecture does seem to hold for periodic closed timelike curves.Partially supported by FCT (Portugal). 1 We use the conventions of [MTW73], including geometrized units (c = G = 1).

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The Rocket Problem in General Relativity

Cited by 9 publications

References 11 publications

Optimal time travel in the Gödel universe

Optimal time travel in the Gödel universe

The optimisation of low-acceleration interstellar relativistic rocket trajectories using genetic algorithms

Optimal Time Travel in the Gödel Universe

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