Dimensional reduction in numerical relativity: Modified cartoon formalism and regularization

Abstract

We present in detail the Einstein equations in the Baumgarte-Shapiro-Shibata-Nakamura formulation for the case of $D$ dimensional spacetimes with $SO(D-d)$ isometry based on a method originally introduced in Ref.1. Regularized expressions are given for a numerical implementation of this method on a vertex centered grid including the origin of the quasi-radial coordinate that covers the extra dimensions with rotational symmetry. Axisymmetry, corresponding to the value $d=D-2$, represents a special case with fewer constraints on the vanishing of tensor components and is conveniently implemented in a variation of the general method. The robustness of the scheme is demonstrated for the case of a black-hole head-on collision in $D=7$ spacetime dimensions with $SO(4)$ symmetry.

25 pages, 2 figures, Special Issue on Selected Papers of the III Amazonian Symposium on Physics

References in corpus (21)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship
• How to move a black hole without excision: gauge conditions for the numerical evolution of a moving puncture
• Binary black-hole evolutions of excision and puncture data
• High-spin binary black hole mergers
• The high-energy collision of two black holes
• Cross section, final spin and zoom-whirl behavior in high-energy black hole collisions
• High-velocity collision of two black holes
• Eccentric binary black-hole mergers: The transition from inspiral to plunge in general relativity
• Ultrarelativistic black hole formation
• Equilibration rates in a strongly coupled nonconformal quark-gluon plasma
• Numerical relativity for D dimensional space-times: head-on collisions of black holes and gravitational wave extraction
• Black-hole production from ultrarelativistic collisions
• Is super-Planckian physics visible? -- Scattering of black holes in 5 dimensions
• The Black Ring is Unstable
• Head-on collisions of unequal mass black holes in D=5 dimensions
• Simulation of Black Hole Collisions in Asymptotically AdS Spacetimes
• Dimensional reduction in numerical relativity: Modified cartoon formalism and regularization
• Higher dimensional Numerical Relativity: code comparison
• Complexified boost invariance and holographic heavy ion collisions
• New frontiers in Numerical Relativity

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• Long-term stable nonlinear evolutions of ultracompact black-hole mimickers
• Numerical Relativity and High Energy Physics: Recent Developments
• Gravitational wave extraction in higher dimensional numerical relativity using the Weyl tensor
• Assessing the stability of ultracompact spinning boson stars with nonlinear evolutions
• Hair is complicated: Gravitational waves from stable and unstable boson-star mergers
• Orbiting black-hole binaries and apparent horizons in higher dimensions
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