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Register a new userHorizons in a binary black hole merger I: Geometry and area increase
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Recent advances in numerical relativity have revealed how marginally trapped surfaces behave when black holes merge. It is now known that interesting topological features emerge during the merger, and marginally trapped surfaces can have self-intersections. This paper presents the most detailed study yet of the physical and geometric aspects of this scenario. For the case of a head-on collision of non-spinning black holes, we study in detail the world tube formed by the evolution of marginally trapped surfaces. In the first of this two-part study, we focus on geometrical properties of the dynamical horizons, i.e. the world tube traced out by the time evolution of marginally outer trapped surfaces. We show that even the simple case of a head-on collision of non-spinning black holes contains a rich variety of geometric and topological properties and is generally more complex than considered previously in the literature. The dynamical horizons are shown to have mixed signature and are not future marginally trapped everywhere. We analyze the area increase of the marginal surfaces along a sequence which connects the two initially disjoint horizons with the final common horizon. While the area does increase overall along this sequence, it is not monotonic. We find short durations of anomalous area change which, given the connection of area with entropy, might have interesting physical consequences. We investigate the possible reasons for this effect and show that it is consistent with existing proofs of the area increase law.
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We study in detail the dynamics and stability of marginally trapped surfaces during a binary black hole merger. This is the second in a two-part study. The first part studied the basic geometric aspects of the world tubes traced out by the marginal surfaces and the status of the area increase law. Here we continue and study the dynamics of the horizons during the merger, again for the head-on collision of two non-spinning black holes. In particular we follow the spectrum of the stability operator during the course of the merger for all the horizons present in the problem and implement systematic spectrum statistics for its analysis. We also study more physical aspects of the merger, namely the fluxes of energy which cross the horizon and cause the area to change. We construct a natural coordinate system on the horizon and decompose the various fields appearing in the flux, primarily the shear of the outgoing null normal, in spin weighted spherical harmonics. For each of the modes we extract the decay rates as the final black hole approaches equilibrium. The late part of the decay is consistent with the expected quasi-normal mode frequencies, while the early part displays a much steeper fall-off. Similarly, we calculate the decay of the horizon multipole moments, again finding two different regimes. Finally, seeking an explanation for this behavior, motivated by the membrane paradigm interpretation, we attempt to identify the different dynamical timescales of the area increase. This leads to the definition of a ``slowness parameter for predicting the onset of transition from a faster to a slower decay.
In this second part of a two-part paper, we discuss numerical simulations of a head-on merger of two non-spinning black holes. We resolve the fate of the original two apparent horizons by showing that after intersecting, their world tubes turn around and continue backwards in time. Using the method presented in the first paper to locate these surfaces, we resolve several such world tubes evolving and connecting through various bifurcations and annihilations. This also draws a consistent picture of the full merger in terms of apparent horizons, or more generally, marginally outer trapped surfaces (MOTSs). The MOTS stability operator provides a natural mechanism to identify MOTSs which should be thought of as black hole boundaries. These are the two initial ones and the final remnant. All other MOTSs lie in the interior and are neither stable nor inner trapped.
The understanding of strong-field dynamics near black-hole horizons is a long-standing and challenging prob- lem in general relativity. Recent advances in numerical relativity and in the geometric characterization of black- hole horizons open new avenues into the problem. In this first paper in a series of two, we focus on the analysis of the recoil occurring in the merger of binary black holes, extending the analysis initiated in [1] with Robinson- Trautman spacetimes. More specifically, we probe spacetime dynamics through the correlation of quantities defined at the black-hole horizon and at null infinity. The geometry of these hypersurfaces responds to bulk gravitational fields acting as test screens in a scattering perspective of spacetime dynamics. Within a 3 + 1 approach we build an effective-curvature vector from the intrinsic geometry of dynamical-horizon sections and correlate its evolution with the flux of Bondi linear momentum at large distances. We employ this setup to study numerically the head-on collision of nonspinning black holes and demonstrate its validity to track the qualita- tive aspects of recoil dynamics at infinity. We also make contact with the suggestion that the antikick can be described in terms of a slowness parameter and how this can be computed from the local properties of the horizon. In a companion paper [2] we will further elaborate on the geometric aspects of this approach and on its relation with other approaches to characterize dynamical properties of black-hole horizons.
In classical numerical relativity, marginally outer trapped surfaces (MOTSs) are the main tool to locate and characterize black holes. For five decades it has been known that during a binary merger, a new outer horizon forms around the initial apparent horizons of the individual holes once they are sufficiently close together. However the ultimate fate of those initial horizons has remained a subject of speculation. Recent axisymmetric studies have shed new light on this process and this pair of papers essentially completes that line of research: we resolve the key features of the post-swallowing axisymmetric evolution of the initial horizons. This first paper introduces a new shooting-method for finding axisymmetric MOTSs along with a reinterpretation of the stability operator as the analogue of the Jacobi equation for families of MOTSs. Here, these tools are used to study exact solutions and initial data. In the sequel paper they are applied to black hole mergers.
In a binary black hole merger, it is known that the inspiral portion of the waveform corresponds to two distinct horizons orbiting each other, and the merger and ringdown signals correspond to the final horizon being formed and settling down to equilibrium. However, we still lack a detailed understanding of the relation between the horizon geometry in these three regimes and the observed waveform. Here we show that the well known inspiral chirp waveform has a clear counterpart on black hole horizons, namely, the shear of the outgoing null rays at the horizon. We demonstrate that the shear behaves very much like a compact binary coalescence waveform with increasing frequency and amplitude. Furthermore, the parameters of the system estimated from the horizon agree with those estimated from the waveform. This implies that even though black hole horizons are causally disconnected from us, assuming general relativity to be true, we can potentially infer some of their detailed properties from gravitational wave observations.
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