Other
Scientific paper
Jun 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phrvd..55.7529s&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 55, Issue 12, 15 June 1997, pp.7529-7537
Other
4
Numerical Relativity, Lower Dimensional Models, Minisuperspace Models
Scientific paper
We study time symmetric initial data sets of pure gravitational waves for 3D numerical relativity. We adopt two types of spatial line elements: one is the Brill wave type, γrr=γθθ/r2, and the other is that the line element of the unit sphere is conformal flat, i.e., γθθ=γφφ/sin2θ. In both cases, the Hamiltonian constraint reduces to the simple 3D elliptic-type equation for the conformal factor which can be accurately solved. We numerically solve the elliptic-type equations for gravitational waves of 22 and 24 poles. For solutions of high amplitude gravitational waves, we determine the apparent horizon encompassing them to investigate criteria of formation of black hole from gravitational collapse of gravitational waves as well as to know the required grid resolution for simulation of the collapse of gravitational waves to be a black hole. It is found that a fine grid of its size <~0.01M for each direction of 3D Cartesian coordinates will be required in numerical simulation.
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