Head-on collisions of black holes


The head-on collision of two equal-mass black holes represents the simplest type of black hole merger because this scenario still has a considerable degree of symmetry. Still, this scenario cannot be studied by analytic methods, and thus can only be analyzed by numerical means.
The figure shows three snapshots of such a numerical simulations we obtained using Dynamic Black Hole Excision. This means, that the excision region follows the motion of the holes across the grid and merges into a single excision region as the holes merge. The figure also shows the horizons surrounding the holes (white grid). These horizons represent a boundary inside which nothing, not even light, can travel outwards. The region inside is therefore cuasally connected from the exterior region. This is why we are allowed to cut out part of the computational domain inside the horizons.

[head-on snapshots]


From top to bottom, the three snapshots represent the key stages of a head-on collision. Initially, the holes are far apart and have distinct horizons. As they approach, a common horizon forms. Finally, the single merged hole rings down while continuing to emit gravitational waves.
The gravitational waves resulting from such a collision need to be calculated at relatively large distance from the black hole, where the distinction between a background spacetime and gravitational waves propagating on this background becomes meaningful. The result for this head-on collision is presented in the following figure.

[waveform]


A convenient measure for the wave signal is the Zerilli Function. In the case of the head-on collision, the signal is dominated by the m=0 quadrupole moment. The corresponding part of the Zerilli function represents the three stages of the simulation. The infall up to about 30 M, a strong pulse originating from the merger and the quasi-normal ring-down of the single hole. The total energy radiated in this scenario is about 0.1 % of the total energy of the two black holes.