R. F. Aranha, I. Damião Soares, E. V. Tonini
We examine numerically the process of gravitational wave recoil in the merger
of two black holes in non head-on collision, in the realm of Robinson-Trautman
spacetimes. Characteristic initial data for the system are constructed, and the
evolution covers the post-merger phase up to the final configuration of the
remnant black hole. The net momentum flux carried out by gravitational waves
and the associated impulses are evaluated. Our analysis is based on the
Bondi-Sachs conservation laws for the energy momentum of the system. The net
kick velocity $V_{k}$ imparted to the merged system by the total gravitational
wave impulse is also evaluated. Typically for a non head-on collision the net
momentum flux carried out by gravitational waves is nonzero for equal-mass
colliding black holes. The distribution of $V_{k}$ as a function of the
symmetric mass ratio $\eta$ is well fitted by a modified Fitchett
$\eta$-scaling law, the additional parameter modifying the law being a measure
of the nonzero gravitational wave momentum flux for equal-mass initial black
holes. For an initial infalling velocity $v/c \simeq 0.462$ of the colliding
black holes, and incidence angle of collision $\rho_0=21^{o}$, we obtain a
maximum $V_{k} \sim 121 {\rm km/s}$ located at $\eta \simeq 0.226$. For initial
equal-mass black holes ($\eta=0.25$) we obtain $V_{k} \sim 107 {\rm km/s}$.
Based on the integrated Bondi-Sachs momentum conservation law we discuss a
possible definition of the center-of-mass velocity of the binary merged system
and show that -- in an appropriate inertial frame -- it approaches
asymptotically the net kick velocity, which is the velocity of the remnant
black hole in this inertial frame. For larger values of $v/c$ we obtain
substantially larger values of the net kick velocity, e.g., for $v/c \simeq
0.604$ a maximum $V_{k} \sim 610 {\rm km/s}$ is obtained.
View original:
http://arxiv.org/abs/1202.1271
No comments:
Post a Comment