Derivation of the relativistic burgers equation on a de sitter background

Date

2014-12-17

Author

Okutmuştur, Baver

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Recently several versions of relativistic Burgers equations have been derived on different spacetime geometries by the help of Lorentz invariance property and the Euler system of relativistic compressible flows on the related backgrounds. The concerning equations on Minkowski (flat) and Schwarzshild spacetimes are obtained in the article [6] where the finite volume approximations and numerical calculations of the given models are presented in detail. On the other hand a similar work on the Friedmann–Lemaˆıtre–Robertson–Walker (FLRW) geometry is described in [3]. In this paper, we consider a family member of FLRW spacetime so-called de Sitter background, introduce some important features of this spacetime with its metric and derive the relativistic Burgers equation on it. The Euler system of equations on de Sitter spacetime can be found by a known process by the help of Christoffel symbols and tensors for perfect fluids. We applied the usual techniques used in [3, 6] to derive relativistic Burgers equations from the Euler system on de Sitter background. By the help of finite volume method on curved spacetimes, we examined the numerical illustrations of the given model in the last part.

Subject Keywords

Relativistic Burgers equations, De Sitter metric, Euler system, Spacetime, Finite volume approximation

URI

http://www.wseas.us/e-library/conferences/2014/Istanbul/AMATH/AMATH-00.pdf
https://hdl.handle.net/11511/77730

Conference Name

International Conference on Applied Mathematics, Mathematics and Computers in Science and Engineering Series, (15 - 17 Aralık 2014)

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Department of Mathematics, Conference / Seminar

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Citation Formats

B. Okutmuştur, “Derivation of the relativistic burgers equation on a de sitter background,” İstanbul, Türkiye, 2014, vol. 38, p. 41, Accessed: 00, 2021. [Online]. Available: http://www.wseas.us/e-library/conferences/2014/Istanbul/AMATH/AMATH-00.pdf.