General Relativistic Simulations of Gravitational Radiation Capture of Black Holes

Abstract

Initially unbounded two black holes (BHs) can be captured by losing the energy through the emission of gravitational waves (GWs) when they experience very close encounter. This is called the gravitational radiation capture (GR capture) process. In this thesis, the GR capture of BHs is investigated with the numerical relativistic (NR) simulations and compared with the Post-Newtonian (PN) approximations. In order to reduce the wasteful computations, we adopt the parabolic approximation which assumes that the GW radiations from the hyperbolic orbit is same with those from the parabolic orbit, because they have almost same paths around the pericenter. The radiated energy and angular momentum from the close encounter between two unequal mass BHs and spinning BHs are investigated for the various initial angular momentum. The impact parameter is also calculated by using the radiated energy from the one-time passage in a fly-by orbit.

At the large initial angular momentum, two BHs have a fly-by orbit. As the initial angular momentum decreases, the pericenter distance becomes shorter and more GWs are emitted. Below a certain initial angular momentum, two BHs have a direct merging orbit, not the fly-by orbit. The most energetic encounters occur around the boundary between the direct merging and the fly-by orbits and they emit several percent of the total energy even from the fly-by orbits. In the case of the fly-by orbit, equal mass BHs emit more GWs than unequal mass BHs at the same initial orbital angular momentum if their total masses are same. For the spinning BHs, the amount of GW radiation is dependent on the inner product between the orbital and spin angular momentum directions. The most GWs are emitted when the spins of both two BHs are anti-aligned with the orbital angular momentum for the case of the fly-by orbit at the same initial orbital angular momentum.

The impact parameters of GR capture have been obtained from the initial orbital angular momenta and the radiated energies in the fly-by orbits. In order to be captured, high energy orbit requires more close encounter, i.e., small impact parameter. Therefore, as the energy of the hyperbolic orbit increases, the impact parameter should be decreased. The decreasing rates of the impact parameters are smaller when the BHs have higher mass ratio and anti-aligned spin directions. At the same orbital energy, the equal mass and anti-aligned spin BHs give larger impact parameters. The impact parameters obtained in NR deviate from the results in the PN if the encounter is strong enough to emit the energy more than 0.01-0.1% of the total energy. In the high energy end, the NR gives larger impact parameters as much as 50-60% than those of the PN.

The GR capture processes including the eccentric merger require very close encounter between the BHs. It is expected to occur in the high density region, such as the vicinity of the supermassive BH in the galactic center. Therefore, its incidence or detection rates can reveal the distribution of BHs there which cannot be inferred by the electromagnetic waves.