Dust content solutions for the Alcubierre warp drive spacetime
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Regular Article - Theoretical Physics
Dust content solutions for the Alcubierre warp drive spacetime Osvaldo L. Santos-Pereira1,a , Everton M. C. Abreu2,3,4,b , Marcelo B. Ribeiro1,4,5,c 1
Instituto de Física, Universidade Federal do Rio de Janeiro–UFRJ, Rio de Janeiro, RJ 21941-972, Brazil Departamento de Física, Universidade Federal Rural do Rio de Janeiro–UFRRJ, Seropédica, RJ 23890-971, Brazil 3 Departamento de Física, Universidade Federal de Juiz de Fora–UFJF, Juiz de Fora, MG 36036-330, Brazil 4 Programa de Pós-Graduação Interdisciplinar em Física Aplicada, Instituto de Física, Universidade Federal do Rio de Janeiro-UFRJ, Rio de Janeiro, RJ 21941-972, Brazil 5 Observatório do Valongo, Universidade Federal do Rio de Janeiro–UFRJ, Rio de Janeiro, RJ 20080-090, Brazil
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Received: 11 June 2020 / Accepted: 14 August 2020 © The Author(s) 2020
Abstract The Alcubierre metric is a spacetime geometry where a massive particle inside a spacetime distortion, called warp bubble, is able to travel at velocities arbitrarily higher than the velocity of light, a feature known as the warp drive. This is a consequence of general relativity, which allows for global superluminal velocities but restricts local speeds to subluminal ones as required by special relativity. In this work we solved the Einstein equations for the Alcubierre warp drive spacetime geometry considering the dust matter distribution as source, since the Alcubierre metric was not originally advanced as a solution of the Einstein equations, but as a spacetime geometry proposed without a source gravity field. We found that all Einstein equations solutions of this geometry containing pressureless dust lead to vacuum solutions. We also concluded that these solutions connect the Alcubierre metric to the Burgers equation, which describes shock waves moving through an inviscid fluid. Our results also indicated that these shock waves behave as plane waves.
1 Introduction In general relativity it is possible for particles, in a global sense, to travel with superluminal velocities whereas the light speed limit is respected inside a local light cone. The Alcubierre warp drive metric [1] satisfies this requirement by basically producing a spacetime distortion, called a warp bubble, such that a particle would travel inside this bubble contracting the spacetime in front of it and expanding the spacetime behind it. In such a geometrical arrangement, the particle travels globally with superluminal velocity whereas the warp a e-mail:
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bubble guarantees that locally the particle’s speed remains subluminal. In its original formulation it was advanced that this warp metric would imply the violation of energy conditions, as well as reportedly requiring great amounts of negative energy density. Following Alcubierre’s original work, several efforts were made to understand the main caveats of the warp drive metric. Ford and Roman [2] advanced some quantum
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