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Abstract: We derive a formalism of numerical relativity for higher-dimensionalspacetimes and develop numerical codes for simulating a wide variety offive-dimensional 5D spacetimes for the first time. First, theBaumgarte-Shapiro-Shibata-Nakamura formalism is extended for arbitraryspacetime dimensions $D \ge 4$, and then, the so-called cartoon method, whichwas originally proposed as a robust method for simulating axisymmetric 4Dspacetimes, is described for 5D spacetimes of several types of symmetries.Implementing 5D numerical relativity codes with the cartoon methods, we performtest simulations by evolving a 5D Schwarzschild spacetime and a 5D spacetimecomposed of a gravitational-wave packet of small amplitude. The numericalsimulations are stably performed for a sufficiently long time, as done in the4D case, and the obtained numerical results agree well with the analyticsolutions: The numerical solutions are shown to converge at the correct order.We also confirm that a longterm accurate evolution of the 5D Schwarzschildspacetime is feasible using the so-called puncture approach. In addition, wederive the Landau-Lifshitz pseudo tensor in arbitrary dimensions, and show thatit gives a robust tool for computing the energy flux of gravitational waves.The formulations and methods developed in this paper provide a powerful toolfor studying nonlinear dynamics of higher-dimensional gravity.



Author: Hirotaka Yoshino, Masaru Shibata

Source: https://arxiv.org/







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