Reissner-Nordström Uzay-zaman Geometrisinde Burgers Modelleri için ¸Sok ve Seyrelme Dalgalarının Yayılımı

Yakın zamanda Burgers denklemlerinin rölativistik modellerinin bir çok çe¸sidi elde edilip, bu modellerin farklı uzay-zaman geometrilerindeki versiyonları da geli¸stirildi. Bu makalede daha önceki çalı¸smalarda kullanılan teknikler geli¸stirilerek Reissner-Nordström uzay-zaman geometrisine uygulandı. Bunun sonucunda, enerji-momentum tensörlerinden yararlanılarak Euler ve rölativistik Burgers denklemleri elde edildi. Uzay-zamanı küresel ve elektrik yüklü bir kitle olarak tasvir eden Reissner-Nordström metri˜ginden elde etti˜gimiz modelimizin statik çözümler içerdi˜gini gözlemledi˜gimiz bu çalı¸smada, bu çözümlerin davranı¸sları da ayrıca etüt edildi. Bunun yanında sonlu hacim metodları kullanılarak ¸sok ve seyrelme dalgalarının yayılımı bir çok nümerik hesapla gösterildi.

Propagations of Shock and Rarefaction Waves on the Reissner-Nordström Spacetimes for Burgers Models

Recently several relativistic versions of Burgers equations are derived and developed on different spacetime geometries. In the current work, we apply the technique used in the recent works to the Reissner-Nordström spacetime geometries. As a result, by using the energy-momentum tensor equations, we obtained the Euler system and then the desired relativistic Burgers models. In this article we observed that the relativistic model, obtained from spherically symmetric, electrically charged Reissner-Nordström metric, contains static solutions. We examined these static solutions and their behaviors in detail. Besides, using the finite volume methods, we analyzed shock and rarefaction wave propagation by several numerical tests.

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