Numerically generated black-hole spacetimes: Interaction with gravitational waves

Abstract

In this paper we present results from a new two-dimensional numerical relativity code used to study the interaction of gravitational waves with a black hole. The initial data correspond to a single black hole superimposed with time-symmetric gravitational waves (Brill waves). A gaugeinvariant method is presented for extracting the gravitational waves from the numerically generated spacetime. We show that the interaction between the gravitational wave and the black hole excites the quasinormal modes of the black hole. An extensive comparison of these results is made to blackhole perturbation theory. For low-amplitude initial gravitational waves, we find excellent agreement between the theoretically predicted t = 2 and t = 4 wave forms and the wave forms generated by the code. Additionally, a code test is performed wherein the propagation of the wave on the black-hole background is compared to the evolution predicted by perturbation theory. PACS number(s): 04.30.+~,95.3O.S1,97.60.Lf I. I N T R O D U C T I O N 45 3544

Towards a singularity-proof scheme in numerical relativity

“…Multiple black holes can be handled by a variation of the HLC. We are beginning to examine these issues now with both the 2D axisymmetric NCSA black hole code [13], and a 3D code using harmonic slicing [24], and will report on this work in future papers.…”

“…Such a line element is easily generalized to one which is suitable for numerical study of axisymmetric spacetimes [13], and it includes both the radial gauge [14] and the quasiisotropic or isothermal gauge [1,15]. In [5], the initial data used in evolving the Schwarzschild geometry are determined by time symmetry and conformal flatness [16], that is, the initial slice is an Einstein-Rosen bridge.…”

Evolution of 3D boson stars with waveform extraction

“…The waveforms are calculated using the Cactus Extract module for the Zerilli function and the Cactus Psikadelia module for 4 with a radial tetrad choice [21]. This particular wave extraction code has been widely used in the past [27][28][29][30][31][32][33].…”

Horizon boundary condition for black hole spacetimes

“…With this coordinate, the throat is located at η = 0. The line element (6) is easily generalized to one which is suitable for numerical studies of axisymmetric spacetimes [1], and it includes both the radial gauge [20] and the quasi-isotropic or isothermal gauge [11,21]. The conformal factor ψ is a function that depends only on η and is specified on the initial time slice so that it satisfies the Hamiltonian constraint with time symmetry and conformal flatness.…”

“…Recent calculations of spacetimes with black holes include simulations of highly distorted black holes [1], colliding black holes [2], the formation of black holes from imploding gravitational waves [3], and balls of collisionless matter [4]. Calculations like these are important stepping stones to full 3D simulations of two coalescing black holes.…”