Numerical relativity forDdimensional axially symmetric space-times: Formalism and code tests

Abstract

The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV gravity scenarios, analysis of the stability of exact solutions and tests of Cosmic Censorship. In order to investigate these questions, we extend numerical relativity to more general space-times than those investigated hitherto, by developing a framework to study the numerical evolution of D dimensional vacuum space-times with anPerforming a dimensional reduction on a (D − 4)-sphere, the D dimensional vacuum Einstein equations are rewritten as a 3+1 dimensional system with source terms, and presented in the Baumgarte, Shapiro, Shibata and Nakamura (BSSN) formulation. This allows the use of existing 3+1 dimensional numerical codes with small adaptations. Brill-Lindquist initial data are constructed in D dimensions and a procedure to match them to our 3+1 dimensional evolution equations is given. We have implemented our framework by adapting the Lean code and perform a variety of simulations of non-spinning black hole space-times. Specifically, we present a modified moving puncture gauge which facilitates long term stable simulations in D = 5. We further demonstrate the internal consistency of the code by studying convergence and comparing numerical versus analytic results in the case of geodesic slicing for D = 5, 6.

Radiation from particles with arbitrary energy falling into higher-dimensional black holes

“…The energy spectrum can be expressed in terms of the wave amplitude at infinity Φ l , given in Eq. (20) of Paper I, as…”

“…This triggered research on the numerical evolution of the full nonlinear Einstein equations in four [10][11][12][13][14][15][16][17][18] and higher dimensions [19][20][21][22][23]. The validation of numerical codes requires semianalytical tools, such as post-Newtonian theory, BH perturbation theory and zero-frequency expansions to model BH collisions.…”

Black holes in a box: Toward the numerical evolution of black holes in AdS space-times

“…Thus, we would like to have a framework that could be used in AdS D , in particular, for D ¼ 5, which is related by the correspondence to four-dimensional gauge theories. The latter issue has been recently addressed by our group in separate publications [39,40], as well as by other groups [41][42][43][44][45][46]. Here we shall focus on the former issue: the active role of boundary conditions.…”

Numerical relativity and high energy physics: Recent developments

“…126,127 It predicts E rad /M = (0.089 ± 0.006)% for equal masses and a monotonic decrease, in good agreement with point particle approximations, as the mass ratio is lowered from q = 1 to smaller values. The numerical method of this work is based on a dimensional reduction by isometry, 128 analogous to the Geroch decomposition. 129 Results from the two different codes have been compared in D = 5, demonstrating excellent agreement.…”