Finite volume approximation of the relativistic Burgers equation on a Schwarzschild--(anti-)de Sitter spacetime

Ceylan, Tuba; Okutmustur, Baver

doi:10.3906/mat-1602-38

Cited by 7 publications

(7 citation statements)

References 6 publications

(30 reference statements)

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“…(3.12) becomes the viscous Burgers equation, valid for a dissipative system, where ν is a diffusion coefficient. It must also be mentioned that the Burgers equation is found in other relativistic solutions as well, such as FLRW cosmology and Schwarzschild background [17]. Based on Eq.…”

Section: Discussionmentioning

confidence: 99%

Dust content solutions for the Alcubierre warp drive spacetime

Santos-Pereira,

Abreu,

Ribeiro

2020

Preprint

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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 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 out 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.

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Section: Discussionmentioning

confidence: 99%

Dust content solutions for the Alcubierre warp drive spacetime

Santos-Pereira,

Abreu,

Ribeiro

2020

Preprint

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“…For the perfect fluid EMT solutions we found that two out of four subcases turn out to be the dust solution of Ref. [19] where both the matter density and the pressure vanish, but the Burgers equation also appears as a result of the solutions of the Einstein equations [29][30][31]. Two other subcases, however, indicate that warp speeds are possible with positive matter density, but at the cost of a complex solution for the warp metric regulating function.…”

Section: Introductionmentioning

confidence: 96%

Fluid dynamics in the warp drive spacetime geometry

2021

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The Alcubierre warp drive metric is a spacetime geometry featuring a spacetime distortion, called a warp bubble, where a massive particle inside it acquires global superluminal velocities, or warp speeds. This work presents solutions of the Einstein equations for the Alcubierre metric having fluid matter as gravity source. The energy–momentum tensor considered has two fluid contents, the perfect fluid and the parametrized perfect fluid (PPF), a tentative more flexible model whose aim is to explore the possibilities of warp drive solutions with positive matter density content. Santos-Pereira et al. (Eur Phys J C 80:786, 2020) already showed that the Alcubierre metric having dust as source connects this geometry to the Burgers equation, which describes shock waves moving through an inviscid fluid, but led the solutions back to vacuum. The same happened for two out of four solutions subcases for the perfect fluid. Other solutions for the perfect fluid indicate the possibility of warp drive with positive matter density, but at the cost of a complex solution for the warp drive regulating function. Regarding the PPF, solutions were also obtained indicating that warp speeds could be created with positive matter density. Weak, dominant, strong and null energy conditions were calculated for all studied subcases, being satisfied for the perfect fluid and creating constraints in the PPF quantities such that a positive matter density is also possible for creating a warp bubble. Summing up all results, energy–momentum tensors describing more complex forms of matter or field distributions generate solutions for the Einstein equations with the warp drive metric where a negative matter density might not be a strict precondition for attaining warp speeds.

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“…(4.12) becomes the viscous Burgers equation, valid for a dissipative system, where ν is a diffusion coefficient. It must also be mentioned that the Burgers equation is found in other relativistic solutions, such as FLRW cosmology and the Schwarzschild background[17][18][19]. Based on Eq.…”

mentioning

confidence: 99%

Dust content solutions for the Alcubierre warp drive spacetime

2020

View full text Add to dashboard Cite

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.

show abstract

Finite volume approximation of the relativistic Burgers equation on a Schwarzschild--(anti-)de Sitter spacetime

Cited by 7 publications

References 6 publications

Dust content solutions for the Alcubierre warp drive spacetime

Dust content solutions for the Alcubierre warp drive spacetime

Fluid dynamics in the warp drive spacetime geometry

Dust content solutions for the Alcubierre warp drive spacetime

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