Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-07-16
Phys.Rev.D80:084025,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
36 pages, 7 figures, minor discussions added, published version
Scientific paper
10.1103/PhysRevD.80.084025
We derive a formalism of numerical relativity for higher-dimensional spacetimes and develop numerical codes for simulating a wide variety of five-dimensional (5D) spacetimes for the first time. First, the Baumgarte-Shapiro-Shibata-Nakamura formalism is extended for arbitrary spacetime dimensions $D \ge 4$, and then, the so-called cartoon method, which was originally proposed as a robust method for simulating axisymmetric 4D spacetimes, is described for 5D spacetimes of several types of symmetries. Implementing 5D numerical relativity codes with the cartoon methods, we perform test simulations by evolving a 5D Schwarzschild spacetime and a 5D spacetime composed of a gravitational-wave packet of small amplitude. The numerical simulations are stably performed for a sufficiently long time, as done in the 4D case, and the obtained numerical results agree well with the analytic solutions: The numerical solutions are shown to converge at the correct order. We also confirm that a longterm accurate evolution of the 5D Schwarzschild spacetime is feasible using the so-called puncture approach. In addition, we derive the Landau-Lifshitz pseudo tensor in arbitrary dimensions, and show that it gives a robust tool for computing the energy flux of gravitational waves. The formulations and methods developed in this paper provide a powerful tool for studying nonlinear dynamics of higher-dimensional gravity.
Shibata Masaru
Yoshino Hirotaka
No associations
LandOfFree
Higher-dimensional numerical relativity: Formulation and code tests does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Higher-dimensional numerical relativity: Formulation and code tests, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Higher-dimensional numerical relativity: Formulation and code tests will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-621170